Question

If the surface area of the two spheres are in the ratio 4:25.then find the ratio of their volumes

Answer 1

Answer:

The ratio of their volume is 8/125.

Step-by-step explanation:

Let s1 be the surface area of 1st sphere.

And

s2 be the surface area of 2nd sphere.

Let r1 be the radius of 1st sphere.

And

r2 be the radius of 2nd sphere.

Surface area of sphere is 4π(r)^2.

Then,

According to the question.

$\\ \frac{s1}{s2} \: = \: \frac{4}{25} \\ \frac{4\pi( {r1}^{2}) }{4\pi( {r2}^{2}) } \: \: = \: \frac{4}{25} \\ \frac{ {r1}^{2} }{ {r2}^{2} } \: = \: \frac{4}{25} \\ \frac{r1}{r2} \: = \: \frac{2}{5}$

Volume of sphere is 4/3πr^3.

Then,

$\frac{v1}{v2} \: = \: \frac{ \frac{4}{3}\pi {r1}^{3} }{ \frac{4}{3} \pi {r2}^{3} } \\ \frac{v1}{v2} \: = \: \frac{ {r1}^{3} }{ {r2}^{3} } \\ \frac{v1}{v2} \: = \: {( \frac{r1}{r2}) }^{3} \\ \frac{v1}{v2} \: \: = \: \: ( { \frac{2}{5}) }^{3} \\ \frac{v1}{v2} \: = \: \frac{8}{125}$

Here,

v1 is the volume of 1st sphere.

And

v2 is the volume of 2nd sphere.

Hence,

Ratio of their volume in 8/125.