Question

a side, s, of the base of the pyramid is 12 meters, and the height, h, is 42 meters. what is the volume of the pyramid in cubic meters?

Explanation:

Step1: Determine the base area

The base of the pyramid is a square with side length \( s = 12 \) meters. The area of a square is \( A = s^2 \).
So, \( A = 12^2 = 144 \) square meters.

Step2: Use the pyramid volume formula

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Ah \), where \( A \) is the base area and \( h \) is the height.
We know \( A = 144 \) and \( h = 42 \), so substitute these values into the formula:
\( V=\frac{1}{3}\times144\times42 \)

First, calculate \( \frac{1}{3}\times144 = 48 \).
Then, \( 48\times42 = 2016 \).

Answer:

The volume of the pyramid is \( 2016 \) cubic meters.