Question

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 a pyramid with 40 m (height), 41 m (slant height), and 18 m (base side length)
what is the volume of the pyramid?
\\(\bigcirc\\) a. \\(240\\,\text{m}^3\\) \\(\bigcirc\\) d. \\(4,320\\,\text{m}^3\\)
\\(\bigcirc\\) b. \\(480\\,\text{m}^3\\) \\(\bigcirc\\) e. \\(4,428\\,\text{m}^3\\)
\\(\bigcirc\\) c. \\(960\\,\text{m}^3\\)

Explanation:

Step1: Calculate the base area (B)

The base is a square with side length 18 m. The area of a square is \( B = s^2 \), where \( s = 18 \) m. So, \( B = 18^2 = 324 \, \text{m}^2 \).

Step2: Identify the height (h)

From the diagram, the height \( h = 40 \) m.

Step3: Apply the volume formula for a pyramid

The volume formula is \( V = \frac{1}{3}Bh \). Substitute \( B = 324 \) and \( h = 40 \):
\( V = \frac{1}{3} \times 324 \times 40 \)
First, calculate \( \frac{1}{3} \times 324 = 108 \). Then, \( 108 \times 40 = 4320 \, \text{m}^3 \).

Answer:

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