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

Answer 1

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Answer 2

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

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

where \(V\) is the volume, the Base Area is the area of the base of the pyramid, and Height is the height of the pyramid.

### Step 1: Calculate the Base Area
The base of the pyramid is a rectangle, and its area can be calculated using the formula:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

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

Now, plug in the values:

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

### Step 2: Use the Volume Formula
We know the volume \(V\) is 231 cubic centimeters, and we just calculated the base area. Now we can plug these values into the volume formula:

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

### Step 3: Solve for Height
First, we need to isolate the height (let's call it \(h\)). To do this, we can start by multiplying both sides of the equation by 3 to get rid of the fraction:

\[
3 \times 231 = 63 \times h
\]

Calculating the left side:

\[
693 = 63h
\]

Next, we divide both sides by 63 to solve for \(h\):

\[
h = \frac{693}{63}
\]

### Step 4: Simplify the Division
Now we need to do the division:

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

### Final Answer
The height of the pyramid is **11 centimeters**.