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?(1 point

Answer 1

wrong bot

Answer 2

The volume \( V \) of a right rectangular pyramid can be calculated using the formula:

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

First, we need to calculate the base area. The base of the pyramid is a rectangle, and its area \( A \) can be calculated as follows:

\[
A = \text{Length} \times \text{Width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]

Calculating the base area:

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

Next, we can use the height of the pyramid, which is given as 22.3 inches, to find the volume:

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

Calculating the volume:

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

First, calculate the product:

\[
69.1875 \times 22.3 = 1545.1875
\]

Now, divide by 3:

\[
V = \frac{1545.1875}{3} = 515.0625 \, \text{cubic inches}
\]

Thus, the volume of the pyramid is:

\[
\boxed{515.0625} \, \text{cubic inches}
\]

Answer 3

I apologize for any errors in my response. Let's recalculate the volume of the right rectangular pyramid step by step:

1. **Calculate the Base Area:**
The base area \( A \) of the rectangular pyramid is given by the product of its length and width.

\[
A = \text{Length} \times \text{Width} = 6.75 \, \text{inches} \times 10.25 \, \text{inches}
\]

\[
A = 69.1875 \, \text{square inches}
\]

2. **Calculate the Volume:**
The volume \( V \) of the pyramid is given by the formula:

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

Substituting the values:

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

First, calculate the product of the base area and height:

\[
69.1875 \times 22.3 = 1545.1875 \, \text{(square inches) \times (inches)} = 1545.1875 \, \text{cubic inches}
\]

Now, divide by 3:

\[
V = \frac{1545.1875}{3} = 515.0625 \, \text{cubic inches}
\]

Thus, the final volume of the pyramid is still:

\[
\boxed{515.0625} \, \text{cubic inches}
\]

If there’s a specific part of the solution you believe is incorrect or if there's additional context that I missed, please let me know!