A storage tank will have a circular base of radius r and a height of r. The tank can be either cylindrical or hemispherical (half a sphere). Complete parts (a) through (e) below. a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, Vequals four thirds pi r cubed and SAequals 4 pi r squared . What is the volume of the hemispherical tank (including the base)? Vequals nothing (Simplify your answer. Type an exact answer in terms of pi .)

Volume:

Ratio:

Step-by-step explanation:

First of all, we need to find the volume of the hemispherical tank.

The volume of a sphere is given by:

where

r is the radius of the sphere

V is the volume

Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:

Now we want to find the ratio between the volume of the hemisphere and its surface area.

The surface area of a sphere is

For a hemisphere, the area of the curved part of the surface is therefore half of this value, so . Moreover, we have to add the surface of the base, which is . So the total surface area of the hemispherical tank is

Therefore, the ratio betwen the volume and the surface area of the hemisphere is