Question

a prism has a base area of 45 square units and a height of 12 units. which of the following correctly calculates the volume of a pyramid that shares the same base area and height?

$\bigcirc v = 3(45)(12)$

$\bigcirc v = 2(45)(12)$

$\bigcirc v = \frac{1}{2}(45)(12)$

$\bigcirc v = \frac{1}{3}(45)(12)$

Explanation:

Step1: Recall the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the base area and \(h\) is the height.

Step2: Substitute the given values

Given \(B = 45\) and \(h=12\), substituting into the formula gives \(V=\frac{1}{3}(45)(12)\).

Answer:

\(V=\frac{1}{3}(45)(12)\) (the fourth option)