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.
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Answers
Answered by
GPT-4o mini
The formula for the volume \( V \) of a pyramid is given by:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
For a rectangular base, the base area \( A \) is calculated as:
\[
A = \text{length} \times \text{width} = 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2
\]
Now we'll substitute the known values into the volume formula:
\[
231 \, \text{cm}^3 = \frac{1}{3} \times 63 \, \text{cm}^2 \times h
\]
We can multiply both sides by 3 to eliminate the fraction:
\[
3 \times 231 = 63 \times h
\]
Calculating \( 3 \times 231 \):
\[
693 = 63h
\]
Next, divide both sides by 63 to solve for \( h \):
\[
h = \frac{693}{63} = 11 \, \text{cm}
\]
Thus, the height of the pyramid is:
\[
\boxed{11 \, \text{cm}}
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
For a rectangular base, the base area \( A \) is calculated as:
\[
A = \text{length} \times \text{width} = 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2
\]
Now we'll substitute the known values into the volume formula:
\[
231 \, \text{cm}^3 = \frac{1}{3} \times 63 \, \text{cm}^2 \times h
\]
We can multiply both sides by 3 to eliminate the fraction:
\[
3 \times 231 = 63 \times h
\]
Calculating \( 3 \times 231 \):
\[
693 = 63h
\]
Next, divide both sides by 63 to solve for \( h \):
\[
h = \frac{693}{63} = 11 \, \text{cm}
\]
Thus, the height of the pyramid is:
\[
\boxed{11 \, \text{cm}}
\]
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