Question

Find the radius of the sphere with the given volume. (a) Volume = 972π mm3 (b) Volume = 4.5π cm3 (c) Volume = 121.5π ft3

Answer 1

(a) r = 9 mm

(b) r = 1.5 cm

(c) r = 4.5 ft

Explanation:

Volume of a sphere is given as;

`V = (4)/(3) \pi r^3`

where;

V is the volume of the sphere

r is radius of the sphere

Make r the subject of the formula;

`V = (4)/(3) \pi r^3\\\\3V = 4\pi r^3\\\\(3V)/(4 \pi) = r^3\\\\r = \sqrt[3]{(3V)/(4 \pi)}`

(a) Volume, V = 972π mm³

`r = \sqrt[3]{(3V)/(4 \pi)} \\\\r = \sqrt[3]{(3*972 \pi)/(4 \pi)}\\\\r = \sqrt[3]{729} \\\\r = 9 \ mm`

(b) Volume, V = 4.5π cm³

`r = \sqrt[3]{(3V)/(4 \pi)} \\\\r = \sqrt[3]{(3*4.5 \pi)/(4 \pi)}\\\\r = \sqrt[3]{3.375} \\\\r = 1.5 \ cm`

(c) Volume, V = 121.5π ft³

`r = \sqrt[3]{(3V)/(4 \pi)} \\\\r = \sqrt[3]{(3*121.5 \pi)/(4 \pi)}\\\\r = \sqrt[3]{91.125} \\\\r = 4.5 \ ft`