Question

A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure.
The volume of the space outside the pyramid but inside the prism is cubic centimeters

Answer 1

The answer is 250 cm³

We need to calculate V = Vr - Vp
V - the volume of the space outside the pyramid but inside the prism
Vr - the volume of the rectangular prism.
Vp - the volume of the pyramid

Vr = w * l * h
w = l = 5 cm
h1 = 12 cm
Vr = 5 * 5 * 12 = 300 cm³


Vp = w * l * h / 3
w = l = 5 cm
h2 = h1/2 = 12/2 = 6 cm
Vp = 5 * 5 * 6 / 3 = 50 cm³


V = Vr - Vp = 300 cm³ - 50 cm³ = 250 cm³

Answer 2

I hope this helps you