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

1 answer

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

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

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

  1. Calculate the area of the base: The base of the pyramid is a rectangle. The area \(B\) can be calculated using the formula:

    \[ B = \text{length} \times \text{width} \] Given the length \(l = 6.75\) inches and the width \(w = 10.25\) inches:

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

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

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

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

    \[ 69.1875 \times 22.3 = 1545.68725 \]

    Now, divide by 3 to find the volume:

    \[ V = \frac{1545.68725}{3} = 515.2290833 \]

  3. Round to the nearest hundredth: Rounding \(515.2290833\) to the nearest hundredth gives:

    \[ 515.23 \]

Thus, the volume of the pyramid is \(\boxed{515.23}\) cubic inches.