CSA of a cuboid – formula – examples

CSA of a cuboid

A cuboid is a three-dimensional object having six rectangular faces in such a way that the opposite faces are identical. 

The curved surface area of a cuboid is the total area of the faces excluding the top and the bottom face.

Curved Surface Area

= Area of faces of the cuboid excluding the top and the bottom face

= Area of 4 faces

= Area of front face + Area of Back face + Area of left-side face + Area of right-side face

= (Length × Height) + (Length × Height) + (Breadth × Height) + (Breadth × Height)

= 2 (Length × Height) +2 (Breadth × Height)

= 2 × Height × ( Length + Breadth )

= 2h (l + b)

Hence the CSA of a cuboid is equal to 2h (l + b), where h, l and b are the height, length and breadth respectively.

Relation between CSA and TSA

CSA is the total area of the 4 faces whereas TSA is the total area of all the 6 faces

CSA + Area of top face + Area of bottom face = TSA

Solved Examples

1. Find the CSA of a cuboid having length, breadth and height as 4 cm, 5 cm and 3 cm respectively.

Solution:

Length = l = 4 cm 

Breadth = b = 5 cm

Height = h = 3 cm

C S A=2 h(l+b)=2 \times 3(4+5)=6 \times 9=54 \mathrm{~cm}^{2}

Therefore, the curved surface area is equal to 54 \mathrm{~cm}^{2}.

2. Find the height of a cuboid having CSA 72 \mathbf{\mathrm{cm}^{2}}. The length and the breadth are 7 cm and 11 cm respectively

Solution:

Length = l = 7 cm 

Breadth = b = 11 cm

Height = h  

Curved Surface area = 72 \mathrm{cm}^{2}.

CSA = 2h (l + b)

⇒ 72 = 2h (7 + 11) = 2h (18) = 36h 

⇒ h = \frac{72}{36} = 2 cm

Therefore, the height of the cuboid is equal to 2 cm.