Question

The pyramid shown has a height of 40 meters a saint height of 41 meters an a square base with a side length of 18 meters
Volume = 1/3 BH
B is the area of the base of the pyramid
H is the height of the pyramid
40 m
41 m
18.
What is the volume of the pyrimid
A. 240m^3
B.480 m^3
C.960m^3
D. 4,320 m^3
E. 4,428 m^3

Answer 1

To calculate the volume of the pyramid, we can use the formula:

\[
\text{Volume} = \frac{1}{3} B H
\]

where:
- \( B \) is the area of the base of the pyramid.
- \( H \) is the height of the pyramid.

Given:
- The base is square with a side length of 18 meters.
- The height \( H \) is 40 meters.

First, we calculate the area of the base \( B \):

\[
B = \text{side length}^2 = 18 \, \text{m} \times 18 \, \text{m} = 324 \, \text{m}^2
\]

Now, we can substitute \( B \) and \( H \) into the volume formula:

\[
\text{Volume} = \frac{1}{3} \times 324 \, \text{m}^2 \times 40 \, \text{m}
\]

Calculating the volume:

\[
\text{Volume} = \frac{1}{3} \times 324 \times 40
\]
\[
= \frac{1}{3} \times 12960
\]
\[
= 4320 \, \text{m}^3
\]

Thus, the volume of the pyramid is:

\[
\boxed{4320 \, \text{m}^3}
\]

So the correct option is **D. 4,320 m³**.