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

1 answer

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.