Question

the pyramid shown has a height of 40 meters, a slant height of 41 meters, and a square base with a side length of 18 meters.
volume = (\frac{1}{3}bh)
b is the area of the base of the pyramid.
h is the height of the pyramid.
image of pyramid
what is the volume of the pyramid?
(\bigcirc) a. (240 \text{m}^3) (\bigcirc) b. (480 \text{m}^3) (\bigcirc) c. (960 \text{m}^3) (\bigcirc) d. (4,320 \text{m}^3) (\bigcirc) e. (4,428 \text{m}^3)

Explanation:

Step1: Calculate the base area (B)

The base is a square with side length 18 meters. The area of a square is side length squared, so \( B = 18 \times 18 = 324 \, \text{m}^2 \).

Step2: Use the volume formula for a pyramid

The volume formula is \( V = \frac{1}{3}Bh \), where \( h = 40 \, \text{m} \) (height of the pyramid) and \( B = 324 \, \text{m}^2 \) (base area). Substitute the values: \( V = \frac{1}{3} \times 324 \times 40 \).
First, calculate \( \frac{1}{3} \times 324 = 108 \). Then, \( 108 \times 40 = 4320 \, \text{m}^3 \).

Answer:

D. \( 4,320 \, \text{m}^3 \)