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