Question

Right Rectangular Prisms & Pyramids Unit Test
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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.(2 points)

Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.


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Answer 1

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

\[
V = \frac{1}{3} \times l \times w \times h
\]

Where:
- \( V \) is the volume of the pyramid,
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

Given:
- Volume \( V = 231 \) cubic centimeters,
- Length \( l = 7 \) cm,
- Width \( w = 9 \) cm.

We can substitute the known values into the formula:

\[
231 = \frac{1}{3} \times 7 \times 9 \times h
\]

First, we calculate \( \frac{1}{3} \times 7 \times 9 \):

\[
7 \times 9 = 63
\]
\[
\frac{1}{3} \times 63 = 21
\]

Now our equation looks like this:

\[
231 = 21 \times h
\]

Next, we solve for \( h \) by dividing both sides of the equation by 21:

\[
h = \frac{231}{21}
\]

Calculating the right side:

\[
h = 11
\]

Thus, the height of the pyramid is:

\[
\boxed{11 \text{ cm}}
\]