Question
A slice of cheese is cut from a wheel of parmesan, n da wdge approximates da shape of a rectangular pyramid. Its base is 4cm wide n 9cm long. Da wedge is 21 cm tall/ Wut is da volume of da piece of cheese?
____ cm3
____ cm3
Answers
GPT-4o mini
To find the volume of the wedge of cheese, which is shaped like a rectangular pyramid, you can use the formula for the volume \( V \) of a pyramid:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
1. **Calculate the Base Area**:
The base area (A) of the rectangular base is calculated as:
\[
A = \text{length} \times \text{width} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2
\]
2. **Use the Height**:
The height (h) of the pyramid is given as 21 cm.
3. **Calculate the Volume**:
Now substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 21 \, \text{cm}
\]
\[
V = \frac{1}{3} \times 756 \, \text{cm}^3
\]
\[
V = 252 \, \text{cm}^3
\]
Thus, the volume of the piece of cheese is **252 cm³**.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
1. **Calculate the Base Area**:
The base area (A) of the rectangular base is calculated as:
\[
A = \text{length} \times \text{width} = 9 \, \text{cm} \times 4 \, \text{cm} = 36 \, \text{cm}^2
\]
2. **Use the Height**:
The height (h) of the pyramid is given as 21 cm.
3. **Calculate the Volume**:
Now substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 36 \, \text{cm}^2 \times 21 \, \text{cm}
\]
\[
V = \frac{1}{3} \times 756 \, \text{cm}^3
\]
\[
V = 252 \, \text{cm}^3
\]
Thus, the volume of the piece of cheese is **252 cm³**.