Question

Describe an informal argument for the volume of a pyramid based on the volume of a cube. A cube has a volume of 12 cubic meters. A square-based pyramid has the same base area and the same height as the cube. What is the volume of the pyramid?(1 point)
Responses

36 m3
36

m
3

36 Meters cubed

4 m3
4

m
3

4 Meters cubed

3 m3
3

m
3

3 Meters cubed

9 m3

Answer 1

A cube can be split into three congruent square-based pyramids: take the corner at (0,0,0) and partition the cube [0,s]^3 by which coordinate (x, y or z) is largest. Each region is a pyramid with base a face of the cube (area s^2) and height s, so each pyramid has volume (1/3)s^3 = (1/3)(volume of cube).

Given the cube's volume is 12 m^3, the pyramid's volume is (1/3)·12 = 4 m^3.