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?

3 answers

To find 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, and \( h \) is the height (altitude) of the pyramid.

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

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

    Substituting the given dimensions:

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

  2. Use the height \( h \): The height of the pyramid is given as \( 22.3 , \text{inches} \).

  3. Substituting \( B \) and \( h \) into the volume formula:

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

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

    \[ 69.1875 \times 22.3 = 1545.68775 \]

    Now, divide by 3:

    \[ V = \frac{1545.68775}{3} \approx 515.22925 \]

Thus, the volume of the pyramid is approximately

\[ \boxed{515.23} , \text{cubic inches} \] (rounded to two decimal places).

It's the wrong answer, give me the correct answer

Let’s re-calculate the volume step by step to ensure we get the correct answer.

Given:

  • Length (l) = 6.75 inches
  • Width (w) = 10.25 inches
  • Height (h) = 22.3 inches

Step 1: Calculate the area of the base (B)

The area \( B \) of the rectangular base is given by:

\[ B = l \times w = 6.75 , \text{inches} \times 10.25 , \text{inches} \]

Calculating \( B \):

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

Step 2: Calculate the volume (V)

Using the volume formula for a pyramid:

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

Substituting the values of \( B \) and \( h \):

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

Step 3: Calculate \(69.1875 \times 22.3\)

\[ 69.1875 \times 22.3 = 1546.6875 \]

Step 4: Calculate the final volume

Now divide by 3:

\[ V = \frac{1546.6875}{3} = 515.5625 \]

Conclusion

Thus, the volume of the pyramid is:

\[ \boxed{515.56} , \text{cubic inches} \]

I apologize for any confusion in my previous calculation. Thank you for your patience!