Question

The ratio of the surface area of two sphere is 3 : 5. What is the ratio of their volumes?

Answer 1

Ratio of their volumes will be 3^3: 5^3

                                                = 27 : 125

Answer 2

Answer:

The ratio of their volumes is 9:25

Step-by-step explanation:

The ratio of the surface area of two sphere is 3 : 5.

Surface area of sphere = $4\pi r^{2}$

So, $\frac{4\pi r^2 }{4 \pi R^2} =\frac{3}{5}$

$\frac{ r^2 }{R^2} =\frac{3}{5}$

$\frac{ r^2 }{R^2} =\frac{3}{5}$

$\frac{ r }{R} =\srt{\frac{3}{5}}$

So, the ratio of the radii is √3:√5

Let the ratio be x

So, the radii are √3x and √5x

Volume of sphere = $\frac{4}{3} \pi r^{3}$

So, Volume of sphere of radius √3x=$\frac{4}{3} \pi (\sqrt{3})^{3}$

So, Volume of sphere of radius √5x=$\frac{4}{3} \pi (\sqrt{5})^{3}$

Ratio of their volumes :

= $\frac{\frac{4}{3} \pi (\sqrt{3})^{3}}{\frac{4}{3} \pi (\sqrt{5})^{3}}$

= $\frac(9}{25}$

Hence the ratio of their volumes is 9:25