Question

The volumes of two-spheres are in the ratio of 8:27. The radius of the smaller sphere is 30 inches. Find the radius of the larger sphere.

Answer 1

45 in

Explanation:

Given 2 similar figures with ratio of radii = a : b , then

ratio of volumes = a³ : b³

Here ratio of volumes = 8 : 27 , then

ratio of radii =
`\sqrt[3]{8}` :
`\sqrt[3]{27}` = 2 : 3

let r be the radius of the larger sphere then by proportion

`(2)/(30)` =
`(3)/(r)` ( cross- multiply )

2r = 90 ( divide both sides by 2 )

r = 45

The radius of the larger sphere is 45 in