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

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

Answer 2

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).

Answer 3

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!