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 equals 1-third B h

B is the area of the base of the pyramid.

h is the height of the pyramid.





Question
What is the volume of the pyramid?

Answer options with 5 options
A.
240 meters cubed

D.
4,320 meters cubed

B.
480 meters cubed

E.
4,428 meters cubed

C.
960 meters cubed

Answer 1

To find the volume of the pyramid, we can use the formula for the volume \( V \) of a pyramid:

\[
V = \frac{1}{3} B h
\]

where \( B \) is the area of the base, and \( h \) is the height of the pyramid.

1. **Calculate the area of the base**:
Since the base is a square with a side length of 18 meters, the area \( B \) can be calculated as:

\[
B = \text{side}^2 = 18^2 = 324 \text{ square meters}
\]

2. **Use the height of the pyramid**:
The height \( h \) of the pyramid is given as 40 meters.

3. **Substitute values into the volume formula**:

\[
V = \frac{1}{3} \times 324 \times 40
\]

Start with the multiplication:

\[
324 \times 40 = 12960
\]

Now, divide by 3:

\[
V = \frac{12960}{3} = 4320 \text{ cubic meters}
\]

Thus, the volume of the pyramid is **4,320 cubic meters**.

The correct answer is **D. 4,320 meters cubed**.