Question

The four diagonals of a cube are drawn to create 6 square pyramids with the same base and height. The volume of the cube is (b)(b)(b). The height of each pyramid is h.

Four diagonals of a cube are drawn to create 6 square pyramids inside of the cube with the same base and height. The sides of the cube have lengths b. The height of each pyramid is h.

Therefore, the volume of one pyramid must equal one-sixth the volume of the cube, or

One-sixth (b)(b)(2h) or One-thirdBh.
One-sixth (b)(b)(6h) or Bh.
One-third (b)(b)(6h) or One-thirdBh.
One-third (b)(b)(2h) or Two-thirdsBh.

Answer 1

Each pyramid has base area B = b^2 and height h, so its volume is (1/3)Bh = (1/3)b^2h.

Since the 6 congruent pyramids fill the cube, (1/3)b^2h = (1/6)b^3. Hence h = b/2 and each pyramid's volume = (1/6)b^3.

(So the correct formula for one pyramid is (1/3)Bh = (1/3)b^2h, which equals 1/6 b^3.)