Here are some volume formulas:

1. If a cone and cylinder have the same radius and the same height, which has the greater volume? Explain or show your reasoning.
2. Suppose you are given a cone, sphere, and cylinder. Find the volume of each solid if the heights of the cone and cylinder are 5 units and all three solids have a radius of 3 units.
3. Suppose you are given another cone, sphere, and cylinder. Find the radius of each figure if the volume is cubic units and the height of the cone and cylinder is 12 units.

A farmer wants to know the sizes of the inside of her barn and silo. Here is the information she has:

• The inside of the barn is 12 meters long and 9 meters wide, two of its walls have a height of 5 meters, and the other two walls measure 7 meters from base to peak.
• The inside of the silo has a radius of 4 meters. It is capped with a hemispherical roof and measures 8 meters from the floor to the top of the dome.

Find the total volume of:

1. The barn.
2. The silo.

Explain or show your reasoning.