Question

A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the:

1. radius of the cylinder
2. curved surface area of the cylinder
   Take π = 3.1

Answer 1

`V = 4/3 pir^3`

Given:

• Radius of sphere r = 6 cm

• π = 3.1

`V = 4/3 xx 3.1 xx 6^3 = 4/3 xx 3.1 xx 216`

`V = (4xx3.1xx216)/3 = 2678.4/3 = 892.8 cm^3`

Volume of cylinder is:

V = πr²h

Let radius of the cylinder = R, height h = 32 cm:

πR²h = 892.8 ⇒ 3.1 × R² × 32 = 892.8

`R^2 = 892.8/(3.1 xx 32) = 892.8/99.2 = 9 => R = sqrt9 = 3 cm`

Radius of the cylinder = 3 cm

CSA = 2πRh = 2 × 3.1 × 3 × 32

= 595.2 cm²