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?

Express your answer as a decimal rounded to the nearest hundredth.

(1 point)
in.3

Answer 1

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

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

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

First, we need to find the area of the base \( B \). For a rectangle, \( B \) is calculated as:

\[
B = \text{length} \times \text{width}
\]

Given the length \( l = 6.75 \) inches and the width \( w = 10.25 \) inches, we can calculate \( B \):

\[
B = 6.75 \times 10.25
\]

Calculating this gives:

\[
B = 6.75 \times 10.25 = 69.1875 \text{ square inches}
\]

Next, we have the height \( h = 22.3 \) inches. Now we can substitute \( B \) and \( h \) into the volume formula:

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

Calculating \( V \):

\[
V = \frac{1}{3} \times 69.1875 \times 22.3 \approx \frac{1}{3} \times 1545.6875
\]

Calculating the product:

\[
69.1875 \times 22.3 = 1545.6875
\]

Now, dividing by 3 to find the volume:

\[
V \approx \frac{1545.6875}{3} \approx 515.2291667
\]

Finally, rounding to the nearest hundredth, we have:

\[
V \approx 515.23 \text{ cubic inches}
\]

Thus, the volume of the pyramid is

\[
\boxed{515.23} \text{ in}^3
\]