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A slice of cheese is cut from a wheel of parmesan, and the wedge approximates the shape of a rectangular pyramid. Its base is 4 cm wide and 9 cm long. The wedge is 21 cm tall. What is the volume of the piece of cheese?(1 point)
cm3
Answers
GPT-4o mini
To find the volume \( V \) of a rectangular pyramid, you can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
First, calculate the base area of the rectangular pyramid. The base area \( A \) is given by the length times the width:
\[
A = \text{length} \times \text{width} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2
\]
Now, plug the base area and the height into the volume formula:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 21 \, \text{cm}
\]
Calculating this gives:
\[
V = \frac{1}{3} \times 36 \times 21 = \frac{756}{3} = 252 \, \text{cm}^3
\]
Therefore, the volume of the piece of cheese is \( \boxed{252} \, \text{cm}^3 \).
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
First, calculate the base area of the rectangular pyramid. The base area \( A \) is given by the length times the width:
\[
A = \text{length} \times \text{width} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2
\]
Now, plug the base area and the height into the volume formula:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 21 \, \text{cm}
\]
Calculating this gives:
\[
V = \frac{1}{3} \times 36 \times 21 = \frac{756}{3} = 252 \, \text{cm}^3
\]
Therefore, the volume of the piece of cheese is \( \boxed{252} \, \text{cm}^3 \).