 #### 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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