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)

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1 answer

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

First, we need to calculate the area of the base of the pyramid, which is a rectangle. The area \( A \) of a rectangle is given by:

\[ A = \text{length} \times \text{width} \]

In this case, the dimensions of the base are:

  • Width = 4 cm
  • Length = 9 cm

So the area of the base is:

\[ A = 4 , \text{cm} \times 9 , \text{cm} = 36 , \text{cm}^2 \]

Next, we plug the area of the base and the height into the volume formula:

  • Base Area = 36 cm²
  • Height = 21 cm

Thus, the volume \( V \) is calculated as follows:

\[ V = \frac{1}{3} \times 36 , \text{cm}^2 \times 21 , \text{cm} \]

Calculating this yields:

\[ V = \frac{1}{3} \times 756 , \text{cm}^3 = 252 , \text{cm}^3 \]

Therefore, the volume of the piece of cheese is:

\[ \boxed{252} , \text{cm}^3 \]