Question

Volume of Pyramids Practice
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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

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

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

First, we need to calculate the base area of the rectangle at the base of the pyramid. The base area (A) can be calculated using:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

Substituting the given values:

\[
\text{Base Area} = 6.75 \, \text{inches} \times 10.25 \, \text{inches} = 69.1875 \, \text{square inches}
\]

Now, we can substitute the base area and height (altitude) into the volume formula:

\[
\text{Volume} = \frac{1}{3} \times 69.1875 \, \text{square inches} \times 22.3 \, \text{inches}
\]

Now, performing the calculations step by step:

1. Calculate the product of base area and height:

\[
69.1875 \times 22.3 = 1546.6875 \, \text{cubic inches}
\]

2. Now divide by 3 to find the volume:

\[
\text{Volume} = \frac{1546.6875}{3} \approx 515.5625 \, \text{cubic inches}
\]

Thus, the volume of the pyramid is approximately \( 515.56 \) cubic inches.