Question

Q 35. The ratio of the volumes of two spheres 27:64. then find the ratio
Of their diameters.

Answer 1

To find the ratio of the surface areas, first we have to find the surface areas with their volumes.

Radius of big sphere = R

Radius of small sphere = r.

Volume of bigger sphere

$\bold{=\frac{4}{3} \pi R^{3}}= </p><p>3</p><p>4</p><p> πR </p><p>3$

Volume of smaller sphere

$\bold{=\frac{4}{3} \pi r^{3}}= </p><p>3</p><p>4</p><p> πr </p><p>3$

Given,

Volume of bigger sphere : Volume of smaller sphere = 64 : 27.

$</p><p>\begin{gathered}\begin{array}{l}{\frac{\frac{4}{3} \pi R^{3}}{\frac{4}{3} \pi r^{3}}=\frac{64}{27}} \\ {\Rightarrow > \frac{R^{3}}{r^{3}}=\frac{64}{27}}\end{array}\end{gathered}$

$=3r3R3=32764=>rR=34$

Surface area of bigger sphere =

$4 \pi R^{2}=4πR </p><p>2</p><p>$

Surface area of smaller sphere =

$4 \pi r^{2}=4πr </p><p>2$

Hence, Surface area of bigger sphere: Surface

area of smaller sphere =

$\begin{gathered}\begin{array}{l}\bold{{=4 \pi R^{2} : 4 \pi r^{2}}} \\ {=\frac{4 \pi R^{2}}{4 \pi r^{2}}=\frac{R^{2}}{r^{2}}} \\ {=\left(\frac{4}{3}\right)^{2}=\frac{16}{9}}\end{array}\end{gathered} </p><p>$

Thus, the ratio of their surface areas = 16 : 9