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:

$$\text{Height}=11,\text{cm}$$