Question

A solid is cylindrical composed with hemispherical ends. If the total height of solid is 100 cm and the height of cylinder is 72 cm, find its total surface area.

Answer 1

Given:

Total height of solid = 100 cm

Height of cylindrical part h = 72 cm

π = `22/7`

The solid is a cylinder with two hemispherical ends.

To Find: Total surface area (TSA) of the solid

Step 1: Find the radius

Total height = height of cylinder + diameter of sphere

100 = 72 + 2r

2r = 100 − 72 = 28

r = 14 cm

Step 2: Write the TSA formula

TSA of solid = Curved surface area of cylinder + Surface area of two hemispheres

TSA = 2πrh + 4πr²

Step 3: Substitute values

(i) Curved surface area of a cylinder

2πrh = 2 × `22/7 xx 14 xx 72`

= 2 × 22 × 2 × 72

= 6336 cm²

(ii) Surface area of two hemispheres

`4πr^2 = 4 xx 22/7 xx 14^2`

`= 4 × 22/7 xx 196`

`= 4 xx 22/7 xx 196`

= 4 × 22 × 28 = 2464 cm²

TSA = 6336 + 2464

= 8800 cm²