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
[tex]\frac{r_1}{r_2}=\frac{1}{4}[/tex]
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
So the ratio of volume is:
[tex]\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r^_2^3} \\ \\ \frac{V_1}{V_2}=(\frac{r_1}{r_2})^3 \\ \\ \frac{V_1}{V_2}=(\frac{1}{4})^3 \\ \\ \frac{V_1}{V_2}=\frac{1}{64} \\ \end{gathered}[/tex]
So the ratio is 1:64
