Question

A wooden article was made by removing out a hemisphere from each end of a solid cylinder. The height and diameter of base of the cylinder are 10 cm and 7 cm respectively, find the total surface area of the remaining solid.

Answer 1

Given:

Height of cylinder, h = 10 cm

Diameter = 7 cm ⇒ r = 3.5 cm

A hemisphere is removed from each end ⇒ the curved surface of 2 hemispheres will be exposed.

Total Surface Area of the remaining solid TSA = CSA of cylinder + CSA of 2 hemispheres

1) CSA of a cylinder

= 2πrh = 2π(3.5)(10) = 70π

2) CSA of 2 hemispheres

CSA of 1 hemisphere = 2πr² 

So, for 2 hemispheres:

= 4πr² = 4π(3.5)² = 4π(12.25) = 49π

3) Total

TSA = 70π + 49π = 119π

Using π = `22/7`.

`119π = 119 × 22/7 = 17 xx 22 = 374`

= 374 cm²