Question

What is the formula for C.S.A of a cuboid?

Answer 1

Hint: We solve this question by explaining the different types of surface areas of the cuboid. We are required to calculate the curved surface area – C.S.A of the cuboid. We need to note that the cuboid does not have any curved surfaces. It has only lateral surface area - L.S.A and total surface area – T.S.A. We need to explain these terms and determine their formula.

Complete step by step solution:
In order to answer this question, let us explain the concept of surface areas for a cuboid. We know a cuboid has no curved surfaces and has only sharp edges. Therefore, the concept of curved surface area - C.S.A does not apply to a cuboid. A cuboid has two surface areas, lateral surface area - L.S.A and total surface area – T.S.A.
Lateral surface area - L.S.A of a cuboid is the sum of the surface areas of all the sides except top and the bottom face. The formula to calculate the lateral surface area is,
$\Rightarrow L.S.A=2\left( lh+bh \right)=2h\left( l+b \right)$
Here, l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid. Now, we explain what the total surface area is.
Total surface area - T.S.A of a cuboid is the sum of the surface areas of all the sides of a cuboid. The formula to calculate the total surface area is given by,
$\Rightarrow T.S.A=2\left( lb+bh+hl \right)$
Here, l is the length of the cuboid, b is the breadth of the cuboid and h is the height of the cuboid.

Note: We need to note that since the cuboid has no curved surfaces, curved surface area C.S.A for a cuboid does not exist. We need to also know these formulae for lateral surface area - L.S.A and total surface area – T.S.A in order to solve many problems based on these concepts.