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?
what is the correct answer
The volume of a pyramid is given by the formula:
\[ V = \frac{1}{3} \times \text{base area} \times \text{altitude} \]
The base of the pyramid is a rectangle with length 6.75 inches and width 10.25 inches. Therefore, the base area is:
\[ \text{base area} = \text{length} \times \text{width} = 6.75 \times 10.25 \]
Substituting the given values into the formula for volume, we get:
\[ V = \frac{1}{3} \times 6.75 \times 10.25 \times 22.3 \]
Simplifying this expression gives us:
\[ V = \frac{4299.375}{3} \times 22.3 \]
\[ V = 1433.125 \times 22.3 \]
\[ V \approx 31977.1875 \]
Therefore, the volume of the pyramid is approximately 31977.1875 cubic inches.