Question

a prism has two times the volume of a pyramid with the same base and altitude.
a. true
b. false

Explanation:

Step1: Recall prism volume formula

Let base area = $B$, altitude = $h$.
Prism volume: $V_{prism}=B\times h$

Step2: Recall pyramid volume formula

Pyramid volume: $V_{pyramid}=\frac{1}{3}B\times h$

Step3: Compare the two volumes

Calculate the ratio: $\frac{V_{prism}}{V_{pyramid}}=\frac{Bh}{\frac{1}{3}Bh}=3$
The prism has 3 times the volume, not 2.

Answer:

B. False