Question

The surface areas of two spheres are in the ratio 16:9. The ratio of their volumes

Answer 1

Your answer is in the image.

Answer 2

Given:

The surface areas of the two spheres are in the ratio of 16:9

To Find:

The ratio of their volumes

Solution:

A sphere is a 3-dimensional figure which is round in shape, the surface of a sphere is calculated by using the formula,

$CSA=4\pi r^2$

So now finding the ratio of radius which will be,

[tex]\frac{4\pi r_1^2}{4\pi r_2^2} =\frac{16}{9} \\ \frac{r_1}{r_2} =\frac{4}{3} [/tex]

Now we can find the ratio of the volume of the sphere, but first, we should know the formula for sphere which is,

$V=\frac{4}{3} \pi r^3$

Now the ratio of the volume will be,

[tex]=\frac{\frac{4}{3}\pi r_1^3 }{\frac{4}{3}\pi r_2^3 } \\\\ =(\frac{r_1}{r_2} )^3\\\\ =\frac{4^3}{3^3} \\\\ =\frac{64}{27} [/tex]

Hence, the ratio of the volume of the sphere will be 64/27.