Find the volume of the sphere in terms of

check the picture below.

so we use the blue triangle to get the slanted length of the isosceles triangle, that means the upper-tangents are each 13 - 5, as you see there, then we use the yellow triangle with those lengths, and the pythagorean theorem to get r.

Look at the picture.

Use the Pythagorean theorem to calculate the length of a side x:

Use the formula of a radius of a circle inscribed in a triangle:

- an area of a triangle

- the sides of the triangle

Calculate:

The fromula of the volume of a sphere:

Substitute: