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(C) Let the radii of the two spheres be $r_1$ and $r_2$ respectively.The surface area of a sphere is given by $S = 4 \pi r^2$.Given the ratio of surfa

Vedclass · Accepted Answer

$8:27$

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(C) Let the radii of the two spheres be $r_1$ and $r_2$ respectively.The surface area of a sphere is given by $S = 4 \pi r^2$.Given the ratio of surface areas: $\frac{4 \pi r_1^2}{4 \pi r_2^2} = \frac{4}{9}$.This simplifies to $\frac{r_1^2}{r_2^2} = \frac{4}{9}$,which implies $\frac{r_1}{r_2} = \sqrt{\frac{4}{9}} = \frac{2}{3}$.The volume of a sphere is given by $V = \frac{4}{3} \pi r^3$.The ratio of their volumes is $\frac{V_1}{V_2} = \frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} = \left(\frac{r_1}{r_2}\right)^3$.Substituting the ratio of radii: $\left(\frac{2}{3}\right)^3 = \frac{8}{27}$.Thus,the ratio of their volumes is $8:27$.

If the surface areas of two spheres are in the ratio $4:9,$ then the ratio of their volumes will be

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