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 answer

To find the volume of a rectangular pyramid, we use the formula:

\[ V = \frac{1}{3} \times B \times h \]

where:

  • \( V \) is the volume,
  • \( B \) is the area of the base,
  • \( h \) is the height.

In this case, the base of the pyramid is rectangular with a width of 4 cm and a length of 9 cm. First, we calculate the area of the base \( B \):

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

The height \( h \) of the pyramid is given as 21 cm. Now we can substitute these values into the volume formula:

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

Calculating the volume:

\[ V = \frac{1}{3} \times 36 \times 21 \]

Calculating \( 36 \times 21 \):

\[ 36 \times 21 = 756 \]

Now, divide by 3:

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

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