Question

The ratio of the volumes of two spheres is 8:7.the ratio of their surface areas is?

Answer 1

Correct question : The ratio of the volumes of two spheres is 8:27. The ratio of their surface areas is?

Answer:

4 : 9

Step-by-step explanation:

We know that ;

Volume of sphere = $\frac{4}{3}$ π r³

Let the radius of two spheres be r₁ and r₂ respectively.

According to the question ;

$\frac{\frac{4}{3} \pi r_1{}^{3}}{\frac{4}{3} \pi r_2{}^{3}}= \frac{8}{27}$

$\frac{r_1{}^{3}}{r_2{}^{3}}= \frac{(2){}^{3}}{(3){}^{3}}$

$\frac{r_1}{r_2} = \frac{2}{3}$

Now, ratio of  surface areas ;

$\frac{4 \pi r_1{}^{2}}{4 \pi r_2{}^{2}}$

$\frac{r_1{}^{2}}{r_2{}^{2}}$

$\frac{2{}^{2}}{3{}^{2}}$

$\frac{4}{9}$

= 4 : 9

Hence, the required ratio is 4 : 9.