Area and volume - Quantitative Aptitude - Aptitude question and answers

Explanation / Important formulas:

Area refers to the space inside a two-dimensional object, like a square or an octagon, while volume refers to the space that a three-dimensional object takes up, or the internal capacity of that object. Units of area include square feet or square meters, while units of volume include cubic feet or cubic meters.

SPHERE

Let the radius of the sphere be r. Then,

  • Volume of the sphere = (4/3 πr3) cubic units
  • Surface area of the sphere = (4πr2) sq. units

CYLINDER

Let radius of base = r and Height (or length) = h. Then,

  • Volume of the cylinder = (πr2h) cubic units
  • Curved surface area of the cylinder = (2πrh) sq. units
  • Total surface area  of the cylinder = 2πr(h + r) sq. units

CUBE

Let each edge of a cube be of length a. Then,

  • Volume of the cube = a3 cubic units
  • Surface area of the cube = 6a2 sq. units
  • Diagonal = 3a units

CUBOID

Let length = l breadth = b and height = h units. Then,

  • Volume of cuboids = (l x b x h) cubic units
  • Surface area of cuboids = 2(lb + bh + lh) sq. units
  • Diagonal = l2 + b2 + h2 units

CONE

Let radius of base = r and Height = h. Then,

  • Slant height, l = h2 + r2 units
  • Volume of the cone = (1/3 π r2h)cubic units
  • Curved surface area = (πrl) sq. units
  • Total surface area = (πrl + πr2) sq. units

HEMISPHERE

Let the radius of a hemisphere be r. Then,

  • Volume of the hemisphere = (2/3 πr3) cubic units
  • Curved surface area of the hemisphere = (2πr2) sq. units
  • Total surface area of the hemisphere = (3πr2) sq. units
  • 1 litre = 1000 cm3

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Test - Area and volume



Area and volume - Question and Answers

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Question 1
The size of a wooden block is 1*5*10 cm3. Find the number of blocks needed to construct a wooden cube of side 50cm.
A
2500
B
500
C
100
D
50
Question 1 Explanation: 
No. of blocks needed = (50*50*50) / (1*5*10) = 2500
Question 2
The size of a wooden block is 2*4*8 cm3. Find the minimum number of such blocks needed to construct a wooden cube?
A
8
B
16
C
32
D
64
Question 2 Explanation: 
A wooden cube constructed from these blocks will have a side of minimum 8cm.
No. of blocks needed = (8*8*8) / (2*4*8) = 8
Question 3
Two cubes of sides 3m, 4m and 5m are melted to form a new cube. The side of the new cube is?
A
12 m
B
10 m
C
8 m
D
6 m
Question 3 Explanation: 
Total volume of the three cubes
= 3cube + 3cube + 5cube = 216 m cube
Side of the new cube = 6m
Question 4
A wooden cube of volume 216 m3 is cut into smaller cubes each of whose side measure 2m. How many smaller cubes have been formed?
A
108
B
54
C
27
D
6
Question 4 Explanation: 
Volume of the smaller cubes = a cube = 8m cube
Number of cubes = 216/8 = 27
Question 5
A cuboid of length 10m, breadth 5m and height 15m is to be formed using cubes of side 5m. How many such cubes are needed to form the cuboid?
A
150
B
50
C
15
D
6
Question 5 Explanation: 
No. of cubes needed
= Volume of the cuboid / volume of a cube
= (10*15*5) / (5*5*5) = 6
Question 6
A cuboid of length 16m, breadth 9m and height 12m is cut into 64 equal smaller cubes. How many do the sides of the cubes measure?
A
1
B
2
C
3
D
6
Question 6 Explanation: 
Volume of the smaller cube = 16*9*12/ 64
= 27 mcube
Side of the smaller cube = 3m
Question 7
A cylinder of radius 5m and height 7m is melted to form 11 equal cuboids. Find the volume of the cuboid?
A
10 m cube
B
20 m cube
C
50 m cube
D
100 m cube
Question 7 Explanation: 
Volume of the cylinder = π r square h = 550 m cube
Volume of the cuboid = 550/11 = 50 m cube
Question 8
The number of revolution a wheel of diameter 21cm takes in travelling a distance of 396m is
A
600 m
B
300 m
C
150 m
D
115 m
Question 8 Explanation: 
No. of revolutions = Distance travelled / Circumference
= 39600 / π d
= 600
Question 9
A metal cube of side 5cm is hammered into a square sheet of thickness 0.2cm. The side of the sheet is?
A
100 cm
B
50 cm
C
25 cm
D
20 cm
Question 9 Explanation: 
Volume of the cube = Volume of the sheet
53 = 0.2*a square
a = 25 cm
Question 10
A man runs around a circular track of radius 70 m at a speed of 5 km/hr. How long does it take for him to complete 20 rounds?
A
0.88 hrs
B
1.76 hrs
C
50.4 hrs
D
61.6 hrs
Question 10 Explanation: 
Circumference of the track = 2* π * 70 m
= 440 m
Time to complete 20 rounds = 20*440/5000
= 1.76 hrs
Question 11
The area of the largest square that can be inscribed in a circle of radius 5cm is?
A
12.5 cm square
B
25 cm square
C
50 cm square
D
100 cm square
Question 11 Explanation: 
Diagonal of the square = Diameter of the circle
√2 a = 2r = 10 cm
a square = 50 cm square
Question 12
In a rectangle hall of length 12m and breadth 8m, the sum of the area of the floor and the ceiling is equal to the sum of the area of the four walls. Find the height of the hall?
A
10 m
B
10 m
C
7.5 m
D
4.8 m
Question 12 Explanation: 
2*12*8 = (2*12h) + (2*8h)
H = 4.8 m
Question 13
The sides of a rectangle are in the ratio 2:3. If the perimeter of the rectangle is 30cm, find its area?
A
30 cm square
B
36 cm square
C
216 cm square
D
180 cm square
Question 13 Explanation: 
2x+3x = 30
X = 6
Area = 12*18 = 216 cm square
Question 14
The area of a rectangle is 108 cm2. If the length of the rectangle is increased by 3 units and its breadth is decreased by 2 units, the area remains unchanged. Find its new perimeter?
A
54 cm
B
56 cm
C
58 cm
D
60 cm
Question 14 Explanation: 
Lb = (l+3) * (b-2)
2(l+b) = 54
Solving the two equations, l = 15cm, b = 12cm
New perimeter = 2*(18+10) = 56cm
Question 15
The capacity of a tank of dimensions 12m*10m*4m is
A
480 liters
B
240 liters
C
240000 liters
D
480000 liters
Question 15 Explanation: 
Volume of the tank = 12*10*4
= 480 cubic meters
Converting cubic meter to liters,
Capacity of the tank = 480*1000
= 480,000 liters
Question 16
If the numerical values of the volume and surface area of a cube are equal, find the length of its edge?
A
6 units
B
36 units
C
12 units
D
10 units
Question 16 Explanation: 
Let the length of its edge be a m
Volume of a cube = a cube cubic units
Surface area = 6 a square Square units
a cube = a square
a = 6 units
Question 17
One side of a rectangle field is 8m and one of its diagonals is 17m. The area of the field is?
A
170m square
B
136m square
C
15m square
D
120m square
Question 17 Explanation: 
I2 + b2 = 17
I2 + b2 = 289
I2 = 289 – 64 = 255
l = 15m
Area = 15*8 = 120 m square
Question 18
The area of a square filed is 20000sq m. A boy crosses the field diagonally at the rate of 4km/hr. find the time taken by the boy to cross the field?
A
6 mins
B
30 mins
C
30 mins
D
5 mins
Question 18 Explanation: 
Side of the field = √20000
= 100 √ 2 m
Diagonal of the field = √ 2 a
= 200 m
Time taken to cross 200 m
= 0.2/4
= 3 minutes
Question 19
A 3cm cube is cut into as many 1cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?
A
3:1
B
1:3
C
1:9
D
27:1
Question 19 Explanation: 
Surface area of a 3 cm cube = 6 *32
= 54 cm square
Surface area of a 1 cm cube = 6*12 = 6 cm square
No. of smaller cubes formed = Volume of large cube /Volume of smaller cube
= 3 cube/ 1 cube
= 27
Ratio = 54/ (27*6)
= 1:3
Question 20
A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 50 sq.ft  per day, then find the approximate number of days taken by the cow to graze the whole field?

 

A
2
B
6
C
12
D
24
Question 20 Explanation: 
The cow can graze the circular area in the middle of the field with radius equal to the length of the rope.
Area which can be grazed by the cow = Π r2
= 616 sq.ft
Area grazed in a day = 50 sq.ft
Time taken to graze 616 sq.ft = 616/50
= 12.13 days
Question 21
If a metal block 2cm*4cm*5.5cm is placed inside a right circular cylinder with a radius of 4cm and a height of 7cm. What percentage of the space inside the cylinder is taken up by the block?
A
6.25%
B
12.5%
C
12.5%
D
22%
Question 21 Explanation: 
Volume of the metal block = lbh cubic units
= 2*4*5.5 = 44 cm square
Volume of the cylinder = Π r2 h cubic units
= (22/7)*(4*4)*7 cm square
= 352 cm square
% of space occupied by the block = (44/352)*100
= 12.5%
Question 22
A 4cm cube is cut into 1cm cubes. Find the % increase in surface area after such cutting?
A
150%
B
600%
C
500%
D
400%
Question 22 Explanation: 
Surface area of a 1cm cube = 6*12 = 6 cm square
No. of smaller cubes formed = Volume of large cube / Volume of smaller cube
= 53 / 13
= 125
Sum of surface areas of smaller cubes = 125*6 = 750 m square
Increase in surface area = 600 m square
% increase = (600/150)*100
= 400%
Question 23
Two cubes of sides 5cm and 7cm are melted together to form a new cube. Find the volume of the new cube?
A
74 cm cube
B
218 cm cube
C
400 cm cube
D
468 cm cube
Question 23 Explanation: 
Volume of the first cube = 53 = 125 cm cube
Volume of the second cube = 73 = 343 cm cube
Volume of the new cube = 125+343 = 468 cm cube
Question 24
If each of the sides of a rectangle are increases by x units. Find the increase in the area?
A
lb +x(l+b)+x square
B
lb +x(l + b)
C
x (l + b)+x square
D
4x
Question 24 Explanation: 
Area of the rectangle = (l + x) (b + x)
= lb+x (l+b) + x square
Increase in area = x (l+b) + x square
Question 25
Raj drives slowly along the perimeter of a rectangle park at 24 kmph and completes one full round in 4min. If the ratio of the length to breadth of the park is 3:2, what are the dimensions?
A
450m X 300m
B
150m X 100m
C
480m X 320m
D
100m X 100m
Question 25 Explanation: 
Raj’s speed = 24 kmph
In 60 mins, he covers 24 km.
In 4 mins, he covers
24000/15 = 1600 m
Perimeter of the park = 1600 m
L: b = 3:2
2(l+b) = 1600
2*(3x+2x) = 1600
X = 160
l = 480m, b = 320m
Question 26
Perimeter of the back wheel is 9 feet and that of the front wheel is 7 feet. On travelling a certain distance, the front wheel makes 10 revolutions more than the back wheel. What is the distance?
A
45 feet
B
63 feet
C
275 feet
D
315 feet
Question 26 Explanation: 
Let the revolutions made by the front wheel be x and that of the back wheel be x-10
X*7 = (x-10)*9
7x= 9x-90
X= 45
Distance = 45*7 = 315 feet
Question 27
The length, breadth and height of a room are in the ratio 3:2:1. The breadth and height are halved, while the length is doubled. Then the total area of the 4 walls of the room will be decreased by

 

A
30%
B
18.75%
C
15%
D
13.6%
Question 27 Explanation: 
Let the length, breadth and height be 3x, 2x and x
Area of the 4 walls = 2h (l+b) = 2x*5x = 10x2
New length, breadth and height = 6x, x, (x/2)
New area = 2*(x/2)*(7x) = 7x2
Decrease in area = 3x2
% decrease = (3x2/10x2)*100
= 30%
Question 28
Nirma makes a popular brand of ice cream in a rectangle shaped bar 6cm long, 5cm wide and 2cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain same, but the length and width will be decreased by some percentage. The new width will be?
A
5.5
B
4.5
C
7.5
D
6.5
Question 28 Explanation: 
Volume of the bar = lbh = 60 cm cube
If the volume is reduced by 19%, new volume = 81% of 60
= 48.6
Let the length and breadth be reduced to x%
((x/100*6)*(x/100)*5)*2 = 48.6
6x2 = 48600
x2 = 8100
x= 90
New width = 90% of 5 = 4.5
Question 29
A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?
A
6K
B
8K
C
12K
D
7K
Question 29 Explanation: 
lw = K
2l*4w = 8lw
8lw – lw = 7lw = 7K
Question 30

The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is

A
3
B
4
C
5
D
6
Question 30 Explanation: 
Perimeter of the square = 4x+8
Perimeter of the triangle = 6x
4x+8 = 6x
X = 4
Question 31
If the radius of a circle is decreased by 20 percent, the area of the circle decreases by
A
16%
B
44%
C
36%
D
40%
Question 31 Explanation: 
Let the radius of the circle be r units and the area be √r2 square units.
New radius = 0.8r
New area = 0.64 √r2
Decrease in area = 0.36 √r2
36% decrease
Question 32
A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in term of x?
A
x2/9
B
x2/8
C
x2/4
D
x2
Question 32 Explanation: 
Let the two sides of the rectangular yard be l feet and b feet.
X feet of fencing covers three sides
x = 2l+b
b = x-2l
Area of the yard = lb square yard
= l(x-2l)
= | x-2 | square
To get the maximum possible value for the area, d (area) / dl = 0
x - 4l = 0
l = x/4
The maximum value for each occurs when l = x/4
b = x = 21 = x/2
Area = (x/4) (x/2)
= x2/ 8
Question 33
How many unit cubes are needed to make a block whose dimensions are 10, 9 and 5?
A
24
B
120
C
240
D
450
Question 33 Explanation: 
No. of cubes needed
= 10*9*5
= 450
Question 34
If the radius of a sphere is doubled, then its volume is increased by?

 

A
100%
B
200%
C
700%
D
800%
Question 34 Explanation: 
V= (4/3) √r3
R = 2r
V = 8*(4/3) √r3
The volume increase by 800%
Question 35

What is the percentage increase in area when a triangle is cloned (so that we have two triangles in total) and the resulting two triangles are joined on their bases form a parallelogram?

A
100%
B
150%
C
300%
D
120%
Question 35 Explanation: 
The area gets doubled since the two triangles are identical
Hence, the area is increased by 100%
Question 36
The volume of a sphere is 88/21*143 cm3. The curved surface of the sphere is?

 

A
2424 cm2
B
2446 cm2
C
2464 cm2
D
2484 cm2
Question 36 Explanation: 
V = (4/3) √r3 = (88/21)*143
R = 14
CSA of a sphere = 4 √r2 = 2464 cm2
Question 37
If the height of a cone is doubled, then its volume is increased by?
A
100%
B
200%
C
300%
D
400%
Question 37 Explanation: 
V = (1/3) √ r2h
If the height is doubled, the volume is also doubled.
Hence, the volume increases by 100%
Question 38
The cost of painting the four walls of a room is Rs 350. The cost of painting a room three times in length, breadth and height will be?
A
Rs. 1050
B
Rs. 1400
C
Rs. 3150
D
Rs. 4200
Question 38 Explanation: 
Let the length, breadth and height of the room be l ,b and h units
Area of the wall 4 walls = 2h (l+b)
If the length, breadth and height are 3l, 3b and 3h,
Area of the 4 walls = 18h (l+b)
Cost = 350*9 = Rs. 3150
Question 39
The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5cm, the height of the cone is?

 

A
10 cm
B
15 cm
C
18 cm
D
24 cm
Question 39 Explanation: 
1/3 √r2h = √r2 h
h = 3h = 15 cm
Question 40

50 men took a dip in water tank 40 m long and 20 m broad on a religious day. If the average displacements of water by a man are 4m3, then the rise in the water level in the tank will be?

A
20 cm
B
25 cm
C
35 cm
D
50 cm
Question 40 Explanation: 
Total displacement of water = 50*4 = 200
40*20*h = 200
H = ¼ m = 25 cm
Question 41
A solid consists of a circular cylinder with an exact fitting right circle cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone, then the height of the cylinder is?

 

A
2h
B
4h
C
2h/3
D
h
Question 41 Explanation: 
Let the height of the cylinder be H
1/3 √r2h + || r2H = 3*(1/3 √r2 h)
h/3 + H = h
H = 2h/3
Question 42
A cube of edge 5cm is cut into cubes of each edge 1cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to?
A
1:5
B
1:25
C
1:125
D
1:625
Question 42 Explanation: 
Ratio = (6*1*1 / 6*5*5)
= 1 : 25
Question 43
A rectangle box is 2m long and 3.5m wide. How many cubic metres of sand are needed to fill the box up to a depth of 12cm?
A
84
B
0.84
C
8.4
D
0.084
Question 43 Explanation: 
Volume needed = 3*3.5*0.12
= 0.84
Question 44
The volume of a cube is 2744 cu.cm. Its surface area is
A
196 cm2
B
784 cm2
C
1176 cm2
D
588 cm2
Question 44 Explanation: 
a cube = 2744
a = 14
62 = 1176 cm2
Question 45
How many cubes of 3cm edge can be cut from a cube of 18cm edge?
A
36
B
216
C
218
D
432
Question 45 Explanation: 
No. of cubes = 18cube / 3cube
= 216
Question 46
A beam 9m long, 40 cm wide and 20 cm high is made up of iron which weight 50 kg per cubic metre. The weight of the beam is
A
56 kg
B
36 kg
C
48 kg
D
27 kg
Question 46 Explanation: 
Weight of the beam = 9*0.4*0.2*50
= 36
Question 47
A circular well with a diameter of 2 meters is dug to a depth of 14 meters. What is the volume of the earth dug out?
A
32 m3
B
36 m3
C
40 m3
D
44 m3
Question 47 Explanation: 
R = d/2 = 1
Volume of earth = √r2 h
= 44 m3
Question 48
Spheres A and B have their radii 40 cm and 10 cm respectively. The ratio of the surface area of A to the surface area of B is?
A
1:4
B
1:16
C
4:1
D
16:1
Question 48 Explanation: 
r1: r2 = 4:1
Surface area is proportional to the square of the radius
A1: A2 = 16: 1
Question 49
The Surface area of a cube is 726 m2. Its volume is
A
1300 m3
B
1331 m3
C
1452 m3
D
1542 m3
Question 49 Explanation: 
6a2= 726
a = 11
Volume = a3 = 1331
Question 50
If each edge of a cube is doubled, then its volume
A
is doubled
B
increases 6 times
C
increases 4 times
D
increases 8 times
Question 50 Explanation: 
V = a3
If the edge is doubled, the volume becomes 8 times
Question 51
The capacity of a tank of dimensions (8 m x 6 m x 2.5 m), is
A
120 liters
B
12000 liters
C
1200 liters
D
120000 liters
Question 51 Explanation: 
8*6*2.5 = 120 m3
= 120000 liters
Question 52
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12cm each. The radius of the sphere is
A
3 cm
B
4 cm
C
6 cm
D
8 cm
Question 52 Explanation: 
4 πr2 = 2 π 6*12
R = 6 cm
Question 53
The diagonals of two squares are in the ratio of 2:5. Find the ratio of their areas?
A
4:25
B
4:15
C
3:25
D
3:15
Question 53 Explanation: 
Area is proportional to the square of the diagonals
Ratio = 4:25
Question 54
The perimeters of two square are 40cm and 32cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
A
22 cm
B
24 cm
C
26 cm
D
28 cm
Question 54 Explanation: 
4a1 = 40
4a2 = 32
a1 = 10
a2 = 8
a square = a1 square – a2 square = 36
a = 6
4a = 24
Question 55
The area of a rectangle is 460 square meters. If the length is 15% more than the breadth, what is the breadth of the rectangular field?
A
18 m
B
20 m
C
22 m
D
25 m
Question 55 Explanation: 
L = 1.15 b
Lb = 460
1.15 b2= 460
b2 = 400
b = 20
Question 56
The ratio between the length and the breadth of a rectangle park is 3:2. If a man cycling along the boundary of the park at the speed of 12km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
A
152600 m2
B
153500 m2
C
153600 m2
D
153800 m2
Question 56 Explanation: 
Perimeter of the park = Distance covered by the man in 8 minutes
= 8*12000/60
= 1600
2 (l+b) = 1600
l+b = 800
l:b = 3:2
Solving, l = 480 b = 320
Area = lb = 153600
Question 57
A cistern 6 m long and 4m wide contains water up to a height of 1m 25cm. Find the total area of the wet surface?
A
42 m2
B
49 m2
C
52 m2
D
64 m2
Question 57 Explanation: 
Area of the wet surface = 2h (l+b) + lb
= 2*1.25(4+6) + 6*4
= 49
Question 58
A spherical lead ball of radius 10cm is melted and small lead balls of radius 5mm are made. The total number of possible small lead balls is
A
800
B
125
C
400
D
8000
Question 58 Explanation: 
No. of balls = (100*100*100) / (5*5*5)
= 8000
Question 59
A rectangular park 60m long and 40m wide has two concrete cross roads running in the middle of the park has been used as a lawn. If the area of the lawn is 2109 sq.m, then what is the width of the road?
A
6 m
B
4 m
C
2 m
D
3 m
Question 59 Explanation: 
Area of the park = (60 x 40) m2= 2400 m2
Area of the lawn = 2109 m2
Area of the cross roads = (2400 - 2109) m2 = 291 m2
Let the width of the road be x meters, Then,
60x+40x- pow(x,2) = 291
x2 – 100x+291 = 0
(x - 97)(x- 3) = 0
x = 3
Question 60
The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, Then the area of the park (in sq.m) is:
A
156300
B
153060
C
153600
D
153006
Question 60 Explanation: 
Perimeter = Distance covered in 8 min = (12000 / 60) x 8m = 1600 m
Let length = 3x meters and breadth = 2x meters
Then, 2(3x +2x) = 1600 or x = 160.
Length = 480 m and breadth = 320 m
Area = (480 x 320)m2 = 153600 m2

Question 61
An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
A
4.04%
B
4.40%
C
4.35%
D
4.53%
Question 61 Explanation: 
A1 = (100x 100)cm2 and A2(102 x 102)cm2
(A2 – A1) = [pow(102,2) – pow(100,2)]
= (102 +100) x (102 - 100)
= 404 cm2
Percentage error = 404/(100 x 100) x 100% = 4.04%
Question 62
A towel when bleached was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:
A
24%
B
30%
C
82%
D
28%
Question 62 Explanation: 
Let original length = x and original breadth = y
Decrease in area
= xy – [(80/100) x] x (90/100) y
= xy – (18/25)xy = (7/25)xy
Decrease% = [(7/25)xy] x [1/(xy)] x100% = 28%
Question 63
What is the least number of square tiles required to pave the floor of a room 15m 17cm long and 9m 2cm broad?
A
148
B
814
C
841
D
418
Question 63 Explanation: 
Length of large tile = H.C.F of 1517 cm and 902 cm = 41 cm
Area of each tile = (41 x 41) cm2
Required number of titles = (1517 x 902) / (41 x 41) = 814

Question 64
The difference between the length and breadth of a rectangle is 23 m .If its perimeter is 206 m, then its area is:
A
5220
B
5202
C
2502
D
2520
Question 64 Explanation: 
We have: (i - b) = 23 and 2(l+b) = 206 or (l+b) = 103
Solving the two equation, we get l = 63 and b = 40
Area = (l x b) = (63 x 40)m2 = 2520 m2
Question 65
The length of a rectangle is halved while its breadth is tripled. What is the percentage change in area?
A
50%
B
40%
C
45%
D
35%
Question 65 Explanation: 
Let original length = x and original breadth = y
Original area = xy
New length = x/2
New breadth = 3y
New area = (x/2) x 3y = (3/2)xy
Increase % = [(1/2(xy))] x (1/xy) x 100% = 50%
Question 66
The length of a rectangle plot is 20 meters more than its breadth. If the cost of fencing the plot @ 26.50 per meters is Rs.5300, What is the length of the plot in metes?
A
50 m
B
60 m
C
45 m
D
75 m
Question 66 Explanation: 
Let breadth = x meters
Then, length = (x+20) meters
Perimeter = (5300/26.50) m = 200 m
2[(x+20) +x] = 200
2x+20 = 100
2x = 80
X = 40
Hence, length = x + 20 = 60 m
Question 67
A rectangular filed is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
A
88 ft
B
77 ft
C
88.5 ft
D
76 ft
Question 67 Explanation: 
We have: l = 20 ft and lb = 680 sq.ft
So, b = 34 ft
Length of fencing = (l+2b) = (20+68) ft = 88 ft.
Question 68
A tank is 25m long, 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq.m is:
A
Rs. 555
B
Rs. 855
C
Rs. 585
D
Rs. 558
Question 68 Explanation: 
Area to be plastered = [2(l+b) x h] +(l x b)
= {[2(25+12) x 6] + (25 x 12)} m2
= (444+300) m2n
= 744m2
Cost of plastering = Rs. 744 x (75/100) = Rs. 558
Question 69
The area of rhombus is 150 cm square. The length of one of the diagonals is 10 cm. The length of the other diagonal is:
A
25 cm
B
30 cm
C
35 cm
D
40 cm
Question 69 Explanation: 
We know the product of diagonals is ½*(product of diagonals)
Let one diagonal be d1 and d2
So as per question
(1/2)*d1*d2 = 150
(1/2)*10*d2 = 150 d2 = 150/5 = 30

Question 70
A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is?
A
350 m
B
300 m
C
200 m
D
250 m
Question 70 Explanation: 
Let the triangle and parallelogram have common base b,
Let the altitude of triangle is h1 and of parallelogram is h2 (which is equal to 100m), then
Area of triangle = (1/2)*b*h1
Area of rectangle = b*h2

As per question (1/2)*b*h1 = b*h2
(1/2)*b*h1 = b*100
h1 = 100*2 = 200m
Question 71
What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle?
A
1:2
B
2:1
C
1:4
D
4:1
Question 71 Explanation: 
Let’s solve this,
Area of rectangle = l*b
Area of triangle = (1/2) l*b
Ratio = l*b : (1/2) l*b = 1:1/2 = 2:1

Question 72
If the area of a square with the side a is equal to the area of a triangle with base a, then the altitude of the triangle is?
A
2a
B
3a
C
4a
D
5a
Question 72 Explanation: 
We know area of square = a2, Area of triangle
= (1/2)*a*h
= (1/2)*a*h = a2 => h= 2a

Question 73
The base of a triangle is 15cm and height is 12cm. The height of another triangle of double the area having the base 20 cm is:
A
20 cm
B
18 cm
C
19 cm
D
16 cm
Question 73 Explanation: 
Area of triangle, A1 = (1/2)*base*height = (1/2)*15*12

= 90 cm2

Area of second triangle = 2*A1 = 180 cm2

(1/2)*20* height = 180

Height = 18 cm
Question 74
The difference of the areas of two squares drawn on two line segments in 32 sq.cm. Find the length of the greater line segment if one is longer than the other by 2cm
A
9 cm
B
6 cm
C
7 cm
D
8 cm
Question 74 Explanation: 
Let the length of the line segments be x and x+2 cm then,
(x+2)2 – x2 = 32 x2 + 4x+4 – x2 = 32
4x = 28 x = 7cm
Question 75
What are the least number of square tiles required to pave the floor of a room 15m 17cm long and 9m 2cm broad?
A
841
B
418
C
481
D
814
Question 75 Explanation: 
So lets solve this,
Length of largest tile = Hcf of (1517 cm and 902 cm)
= 41 cm
Required number of titles = Area of floor/ Area of tile

= (1517 x 902) / (41 x 41) = 814
Question 76
A courtyard is 25 meter long and 16 meters a board is to be paved with bricks of dimensions 20 cm by 10cm. The total number of bricks required is:
A
20000
B
30000
C
25000
D
22000
Question 76 Explanation: 
Number of bricks = Courtyard area / 1 brick area = (2500 x 1600) / (20 x 10) = 20000
Question 77
A circular path of 13m radius has marginal walk 2m wide all round it. Find the cost of levelling the walk at 25p per m2?
A
Rs.45
B
Rs.78
C
Rs.44
D
Rs.40
Question 77 Explanation: 
P (pow(15,2) – pow(13,2)) = 176
176 * ¼ = Rs.44
Question 78
The radius of the two circular fields is in the ratio 3:5 the area of the first field is what percent less than the area of the second?
A
50%
B
60%
C
64%
D
84%
Question 78 Explanation: 
R = 3 p*r*r = 9
R = 5 p*r*r = 25
25 p – 16 p
100 ----? => 64%
Question 79
A rope of which a calf is tied is increased from 12m to 23m, how much additional grassy ground shall it graze (in meter sq)?
A
1120
B
1220
C
1210
D
1250
Question 79 Explanation: 
p (pow{23,2} – pow{12,2}) = 1210

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