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 it into paragraphs.

Answer 1

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

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

First, let's find the area of the base. The base is a rectangle, so we can calculate its area by multiplying the length and the width.

Given:
- Length = 7 cm
- Width = 9 cm

Now, we calculate the base area:

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

Next, we know the volume of the pyramid is 231 cubic centimeters. We can plug the base area into the volume formula and solve for the height.

The volume formula becomes:

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

To eliminate the fraction, we can multiply both sides by 3:

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

Calculating the left side gives us:

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

Now we need to isolate the height. We can do this by dividing both sides by 63:

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

Now we just perform the division.

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

So, the height of the pyramid is 11 cm.