Right Rectangular Prisms & Pyramids Unit Test

Question

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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:

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