Question

If the ratio of volume Is the ratio of volume of two spheres is 1 ratio 8 find ratio of their surface area If the ratio of volumes of two sphere is 1 ratio 8 find ratio of their surface areas

Answer 1

Dear student,
Ratio of volumes is $1:8$
Let the radius of first sphere is a and second sphere is b respectively.
So,
​​​​$\frac{{\displaystyle \frac{4}{3}{\mathrm{\pi a}}^3}}{\frac{4}{3}\pi b^3}=\frac{1}{8}\Rightarrow \frac{a^3}{b^3}=\frac{1}{8}\Rightarrow \frac{{\displaystyle a}}{{\displaystyle b}}=\frac{{\displaystyle 1}}{{\displaystyle 2}}$
Then the ratio of the surfaces areas of the spheres is,
$\frac{{\displaystyle 4{\mathrm{\pi a}}^2}}{4\pi b^2}=\frac{a^2}{b^2}=\frac{{\displaystyle 1}}{{\displaystyle 2^2}}=\frac{1}{4}$

Regards