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.

Answer 1

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

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

We know the volume (V) is 231 cm³, the length (L) is 7 cm, and the width (W) is 9 cm.

First, we need to find the base area:

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

Now, plug the base area and the volume into the volume formula:

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

To get rid of the \(\frac{1}{3}\), multiply both sides by 3:

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

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

Next, divide both sides by 63 to solve for the height:

\[ \text{Height} = \frac{693}{63} = 11 \]

So, the height of the pyramid is:

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