Question

The ratio of volume of two spheres is 8:1. What is the ratio of their radii

​

Answer 1

Answer:

The ratio of volume of two spheres is 8:1. What is the ratio of their radii ​

Volume of sphere B = (4/3)pi*R^3 = 27 (4/3)pi cubic units. So radius of sphere A = 8^(1/3) = 2 units.

Answer 2

Given:

The ratio of volume of 2 spheres = 8 : 1

To Find:

The ratio of the radii

Explanation:

The relationship between the volume and the radii is as follow:

$\dfrac{\text{Volume 1}}{\text{Volume 2}} = \bigg (\dfrac{\text{Radius 1}}{\text{Radius 2}} \bigg)^3$

Solution

$\dfrac{\text{Volume 1}}{\text{Volume 2}} = \bigg (\dfrac{\text{Radius 1}}{\text{Radius 2}} \bigg)^3$

Given that the ratio of the volume is 8 : 1:

$\dfrac{\text{8}}{\text{1}} = \bigg (\dfrac{\text{Radius 1}}{\text{Radius 2}} \bigg)^3$

Find the ratio of the radii:

$\bigg (\dfrac{\text{Radius 1}}{\text{Radius 2}} \bigg)^3 = \dfrac{\text{8}}{\text{1}}$

$\dfrac{\text{Radius 1}}{\text{Radius 2}} = \sqrt[3]{\dfrac{\text{8}}{\text{1}} }$

$\dfrac{\text{Radius 1}}{\text{Radius 2}} = \dfrac{2}{1}$

Answer: The ratio of the radii is 2 : 1