Question

The radii of two spheres are in a ratio of 1:4.What is the ratio of their volumes?

Answer 1

Given:

The radii of the two spheres are in a ratio of 1:4

Find-:

The ratio of their volume

Explanation-:

Radii of two spheres are in a ratio is 1:4

`(r_1)/(r_2)=(1)/(4)`

The volume of a sphere is:

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

So the ratio of volume is:

`\begin{gathered} (V_1)/(V_2)=((4)/(3)\pi r_1^3)/((4)/(3)\pi r^_2^3) \\ \\ (V_1)/(V_2)=((r_1)/(r_2))^3 \\ \\ (V_1)/(V_2)=((1)/(4))^3 \\ \\ (V_1)/(V_2)=(1)/(64) \\ \end{gathered}`

So the ratio is 1:64