Question

A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work. Make into a simplified version. make sound like an 8th grader. Make short.Make copyaable.

Answer 1

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

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

For a rectangular pyramid, the base area is length times width:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

Given:

- Length = 7 cm
- Width = 9 cm
- Volume (V) = 231 cm³

First, we find the base area:

\[
\text{Base Area} = 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2
\]

Now, we can plug the base area into the volume formula:

\[
231 = \frac{1}{3} \times 63 \times \text{Height}
\]

To isolate the height, we can first multiply both sides by 3:

\[
3 \times 231 = 63 \times \text{Height}
\]

Calculating the left side:

\[
693 = 63 \times \text{Height}
\]

Now, divide both sides by 63:

\[
\text{Height} = \frac{693}{63}
\]

Calculating:

\[
\text{Height} = 11 \, \text{cm}
\]

So, the height of the pyramid is:

**Height = 11 cm**