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)

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1 answer

To find the volume of a rectangular pyramid (which is the shape of the cheese wedge), you can use the formula for the volume of a pyramid:

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

First, calculate the base area of the rectangular base:

\[ \text{Base Area} = \text{length} \times \text{width} = 9 , \text{cm} \times 4 , \text{cm} = 36 , \text{cm}^2 \]

Next, substitute the base area and the height into the volume formula. The height of the pyramid is given as 21 cm.

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

Now, calculate the volume:

\[ V = \frac{1}{3} \times 36 \times 21 \] \[ V = \frac{1}{3} \times 756 \] \[ V = 252 , \text{cm}^3 \]

Therefore, the volume of the piece of cheese is \( 252 , \text{cm}^3 \).