Question

Michelle creates a cube with a height of 6 centimeters. Her friend Tasha creates a square-based pyramid with the same height and base area as Michelle’s cube. Find the volume of Michelle’s cube and use it to find the volume of Tasha’s pyramid. Show all work.

Answer 1

Step 1 — Cube
- Side length = height = 6 cm.
- Volume of a cube = side^3 = 6^3 = 216.
- So Volume(cube) = 216 cm^3.

Step 2 — Pyramid
- The pyramid is square-based with the same base area as the cube’s face: base area = 6^2 = 36 cm^2.
- Height = 6 cm.
- Volume of a pyramid = (1/3) × (base area) × (height) = (1/3) × 36 × 6 = (1/3) × 216 = 72.
- So Volume(pyramid) = 72 cm^3.

Answers: cube = 216 cm^3; pyramid = 72 cm^3.