Question

Six pyramids are shown inside of a cube. The height of the cube is h units. The lengths of the sides of the cube are b.
The area of the base of the cube, B, is
square units.

The volume of the cube is
cubic units.

The height of each pyramid, h, is
. Therefore,

b = 2h.

There are
square pyramids with the same base and height that exactly fill the given cube.

Therefore, the volume of one pyramid is
or One-thirdBh.

Answer 1

Fill-ins:

- The area of the base of the cube, B, is b^2 square units.
- The volume of the cube is b^3 cubic units.
- The height of each pyramid, h, is b/2. Therefore b = 2h.
- There are 6 square pyramids with the same base and height that exactly fill the given cube.
- Therefore, the volume of one pyramid is b^3/6 or (1/3)Bh (since B = b^2 and h = b/2, (1/3)b^2(b/2) = b^3/6).