Question

The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is

विकल्प

• 1 : 2

• 2 : 3

• 9 : 16

•  16 : 9

Answer 1

Ist sphere

${\displaystyle V_1=\frac{4}{3}\pi r_1^2}$…… (i)

IInd sphere

${\displaystyle V_2=\frac{4}{3}\pi r_2^3}$…… (ii)

Divide (i) by (ii) we get,

${\displaystyle \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3}}$

${\displaystyle \frac{64}{27}={\left(\frac{r_1}{r_2}\right)}^3}$

${\displaystyle \frac{r_1}{r_2}=\sqrt{\frac{64}{27}}}$

${\displaystyle \frac{r_1}{r_2}=\frac{4}{3}}$

Now, the ratio of their C.S.A

${\displaystyle \frac{S_1}{S_2}=\frac{4\pi r_1^2}{4\pi r_2^2}={\left(\frac{r_1}{r_2}\right)}^2}$

${\displaystyle \frac{S_1}{S_2}={\left(\frac{4}{3}\right)}^2=\frac{16}{9}}$

Hence, ${\displaystyle S_1:S_2=16:9}$