Question

cool down

1. explain how these pictures relate to finding the volume of a pyramid?
2. therefore, imagine that the rectangular prism has a volume of $300\text{ in}^3$, therefore whats the volume of one of the pyramids?

Explanation:

Step1: Relate prism to pyramids

The rectangular prism can be decomposed into 3 congruent pyramids (as shown in the images) that have the same base area and height as related sections of the prism. This means the volume of the prism is equal to the sum of the volumes of the 3 identical pyramids.

Step2: Set up volume relationship

Let $V_p$ = volume of one pyramid, $V_r$ = volume of the rectangular prism.
$V_r = 3V_p$

Step3: Solve for pyramid volume

Rearrange to solve for $V_p$: $V_p = \frac{V_r}{3}$
Substitute $V_r = 300 \text{ in}^3$:
$V_p = \frac{300}{3}$

Answer:

1. The images show that a rectangular prism can be split into 3 congruent pyramids, so the volume of one pyramid is $\frac{1}{3}$ the volume of the prism with a matching base and height.
2. $100 \text{ in}^3$