Question

the surface areas of two spheres are in the ratio 16:9 the ratios of thgeir volume is

Answer 1

Let
$$\begin{gathered} r_1=radiusoffirstsphere \\ {r}_2=radiusofsecondsphere \\ now, \\ \frac{surfaceareaoffirstsphere}{surfaceareaofsecondsphere}=\frac{16}{9} \\ \Rightarrow \frac{4{{\mathrm{\pi r}}_1}^2}{4{{\mathrm{\pi r}}_2}^2}=\frac{16}{9} \\ \Rightarrow \frac{r_1}{r_2}=\frac{4}{3}....\left(1\right) \\ \frac{vol.offirstsphere}{vol.ofsecondsphere}=\frac{{\displaystyle \frac{4}{3}}{{\mathrm{\pi r}}_1}^3}{{\displaystyle \frac{4}{3}}{{\mathrm{\pi r}}_2}^3}={\left[\frac{r_1}{r_2}\right]}^3={\left[\frac{4}{3}\right]}^3=\frac{64}{27} \end{gathered}$$