Question

Question
A right rectangular pyramid has an altitude of 22.3 inches, a length of 6.75 inches, and a width of 10.25 inches. What is the volume of the pyramid in cubic inches?

Answer 1

514.29

Answer 2

To calculate the volume of a right rectangular pyramid, you can use the formula:

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

where:
- \( V \) is the volume,
- \( B \) is the area of the base,
- \( h \) is the height (altitude) of the pyramid.

In this case, the base of the pyramid is a rectangle with a length of 6.75 inches and a width of 10.25 inches.

First, calculate the area of the base:

\[
B = \text{length} \times \text{width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]

\[
B = 69.1875 \, \text{square inches}
\]

Next, we plug the area of the base and the height into the volume formula. The height \( h \) is given as 22.3 inches:

\[
V = \frac{1}{3} \times 69.1875 \, \text{inches}^2 \times 22.3 \, \text{inches}
\]

Calculating that:

\[
V = \frac{1}{3} \times 69.1875 \times 22.3
\]

First, calculate \( 69.1875 \times 22.3 \):

\[
69.1875 \times 22.3 = 1545.1875
\]

Now, divide by 3:

\[
V \approx \frac{1545.1875}{3} \approx 515.0625
\]

Thus, the volume of the pyramid is approximately:

\[
\boxed{515.06} \text{ cubic inches}
\]