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.