Volume and Surface area – Concepts and Formula

Volume and Surface area – Concepts and Formula

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

Total surface area

Total surface area refers to the area including the base(s) and the curved part. It is total of the area covered by the surface of the object. If the shape has curved surface and base, then total area will be the sum of the two areas.

Curved surface area/Lateral surface area

Curved surface area refers to the area of only the curved part of the shape excluding its base(s). It is also referred to as lateral surface area for shapes such as a cylinder.

Volume

The amount of space, measured in cubic units, that an object or substance occupies is called volume. Two-dimensional doesn’t have volume but has area only. For example, Volume of Circle cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

Cube

Let each edge of a cube be of length a, then

Volume = (side)³ = a³ cubic units.
Surface Area = 6 x (Area of one face )² = 6a² sq. units.

Cuboid

Let length = l, breadth = b and height = h units. Then,
Volume = length x breadth x height = ( l x b x h ) cubic units

Surface area = 2 (lb + bh + lh) sq. units.

Cylinder

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

Cone

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

Sphere

Let the radius of the sphere be r. Then,

Hemi sphere

Question Find the volume and surface area of a cuboid 12 m long, 8 m broad and 5 m high.
Answer.Volume = 12 x 8 x 5 = 480 m³
Surface area = 2 ( 12 x 8 + 8 x 5 + 5 x 12 )
= 2 ( 96 + 40 + 60 )
= 2 (196)
= 392

QuestionsThe diagonal of a cube is cm. Find its volume and surface area.
Answer.Let the edge of the cube be a.

Surface Area = 6a² = 6.8² = 6 x 64 = 384

Question. A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and breadth of the reservoir is 3.5 m, then the depth of the reservoir will be ?
Answer.Volume = 42000 = 42m³
Let the depth be h
Volume = 6 x 3.5 x h
42 = 21 x h
h = 42 / 21 = 2 m

Question. The radii of two spheres are in the ratio 3 : 2. What is ratio of their volume ?
Answer. Let the radius is R1 and R2

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