The volumes of the two spheres are in a ratio of 1:8. What is the ratio of their radii?

Solution:

Given, the volume of the two spheres are in a ratio of 1:8

V₁/V₂ = 1:8

We have to find the ratio of their radii.

The volume of the sphere is given by

 V = (4/3)πr³

Let the radius of the first sphere be r₁

The radius of the other sphere be r₂

The volume of the first sphere is V₁ = (4/3)πr₁³

The volume of other sphere is V₂ = (4/3)πr₂³

To find the ratio of radii

V₁/V₂ = (4/3)πr₁³/(4/3)πr₂³

(4/3)πr₁³/(4/3)πr₂³ = 1/8

r₁³/r₂³ = 1/8

Taking cube root,

r₁/r₂ = 1/2

Therefore, the ratio of the radii is 1:2

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The volumes of the two spheres are in a ratio of 1:8. What is the ratio of their radii?

Summary:

The volumes of the two spheres are in a ratio of 1:8. The ratio of their radii is 1:2