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

Answer: The first choice.

Reason: The cube splits into 6 congruent pyramids, so one pyramid has volume (1/6)b^3. The pyramid formula is (1/3)Bh with B = b^2, and since the cube side equals 2h, b^3 = b^2(2h). Thus
(1/6)b^2(2h) = (1/3)b^2h = (1/3)Bh,
which matches the first option.