# 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

V_{1}/V_{2} = 1:8

We have to find the ratio of their radii.

The volume of the sphere is given by

V = (4/3)πr^{3}

Let the radius of the first sphere be r_{1}

The radius of the other sphere be r_{2}

The volume of the first sphere is V_{1} = (4/3)πr_{1}^{3}

The volume of other sphere is V_{2} = (4/3)πr_{2}^{3}

To find the ratio of radii

V_{1}/V_{2} = (4/3)πr_{1}^{3}/(4/3)πr_{2}^{3}

(4/3)πr_{1}^{3}/(4/3)πr_{2}^{3 }= 1/8

r_{1}^{3}/r_{2}^{3} = 1/8

Taking cube root,

r_{1}/r_{2} = 1/2

Therefore, the ratio of the radii is 1:2

## 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

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