Question

If the volume of a sphere is 179 `2/3 cm^3` find its surface area.

Answer 1

Given:

Volume of sphere

V = 179 `2/3 cm^3 = (539)/(3) cm^3`

To Find: Surface area of the sphere.

1) Volume of a sphere

`V = 4/3πr^3`

`539/3 = 4/3 πr^3`

Multiply both sides by 3:

539 = 4πr³

Take π = `22/7`

`539 = 4 × 22/7 r^3 = 88/7 r^3`

`r^3 = 343/8 ⇒ r = root3 (343/8) = 7/2 = 3.5 cm`

2) Surface area of a sphere

S = 4πr²

`S = 4 xx 22/7 xx (3.5)^2`

(3.5)² = 12.25

S = 4 × `22/7` × 12.25

= 154 cm²