Question

Ahmad constructs a square-based pyramid and a cube out of newspaper. The two figures have the same height and the same base area. What is the volume of the pyramid if the volume of the cube is 54 cubic units?(1 point)

36 cubic units

6 cubic units

90 cubic units

18 cubic units

Answer 1

Let the cube have side length s. Then its volume is s^3 = 54, and its base area is s^2 and height is s. The pyramid has the same base area and height, so its volume is

(1/3) × base area × height = (1/3) × s^2 × s = (1/3) s^3 = (1/3) × 54 = 18.

Answer: 18 cubic units.