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The volume of two spheres are in the ratio 64:27. The ratio of there surface area is

Posted by Krishna Kumar 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 7 months ago

Suppose {tex}r_1\ and\ r_2{/tex} be the radii of two spheres.
{tex}\therefore{/tex} the ratio of their volumes = {tex}\frac{\frac{4}{3} \pi r_{1}^{3}}{\frac{4}{3} \pi r_{2}^{3}}=\frac{64}{27}{/tex}
{tex}\left(\frac{r_{1}}{r_{2}}\right)^{3}=\left(\frac{4}{3}\right)^{3}{/tex} {tex}\Rightarrow{/tex} {tex}\frac{r_{1}}{r_{2}}{/tex} = {tex}\frac{4}{3}{/tex}
Ratios of surface areas of two spheres = {tex}\frac{4 \pi r_{1}^{2}}{4 \pi r_{2}^{2}}{/tex}
{tex}=\left(\frac{r_{1}}{r_{2}}\right)^{2}{/tex} = ({tex}\frac{4}{3}{/tex})² = {tex}\frac{16}{9}{/tex}
{tex}\therefore{/tex}Required ratio {tex}= 16: 9.{/tex}

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