Mensuration 3D

If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.These are called Three dimensional as they have depth, breadth and length. Mensuration 3D deals with shapes like cube, cuboid, sphere etc. The problems are generally based on volume and surface area.

Cuboid
Let the length, breadth and height of the cuboid be ‘L’, ‘B’ and ‘H’ respectively.

• Volume = L x B x H
• Curved Surface area = 2 H (L + B)
• Total surface area = 2 (L B + B H + H L)
• Length of diagonal = (L² + B² + H²)^1/2

Cube
Let the side of the cube be ‘a’

• Volume = a³
• Curved Surface area = 4 a²
• Total surface area = 6 a²
• Length of diagonal =  

Example 1: Find the total surface area of the cuboid with dimensions 2 inches × 3 inches × 7 inches.

Solution: Total Surface Area(TSA) = 2 (lb + bh + hl )

TSA = 2 ( 2×3 + 3×7 + 7×2)

TSA = 2 ( 6 + 21 + 14 )

TSA = 82 sq. inch

So, the total surface area of this cuboid is 82 inches²

Example 2:  The length, width and height of a cuboid are 12 cm, 13 cm and 15 cm, respectively. Find the lateral surface area of a cuboid.

Solution: Lateral surface area of a cuboid is given by:

LSA = 2h ( l + w )

LSA = 2×15 ( 12 + 13 )

LSA = 750 cm²

Example 3: Find the surface area of a cube having its sides equal to 8 cm in length.

Solution: Given length, ‘a’= 8 cm

Surface area = 6a²

= 6× 8²

= 6 ×64

= 384 cm²