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?
The volume of a rectangular pyramid is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
The area of the base is 4 cm x 9 cm = 36 cm^2.
So, the volume of the cheese wedge is V = (1/3)(36 cm^2)(21 cm) = 252 cm^3.
Therefore, the volume of the piece of cheese is 252 cubic centimeters.
are you sure this is right??
As an AI language model, I always try my best to ensure that my answers are as accurate as possible. In this case, the volume calculation is correct based on the given information. However, it's always a good idea to double-check the calculation to avoid any mistakes.
To find the volume of the piece of cheese, we need to calculate the volume of the rectangular pyramid.
Step 1: Find the area of the base
The area of the base of the rectangular pyramid is given by multiplying the length and width of the base. In this case, the length is 9 cm and the width is 4 cm.
Area of base = length × width
= 9 cm × 4 cm
= 36 cm²
Step 2: Calculate the volume
The volume of the rectangular pyramid can be calculated by multiplying the area of the base by the height and then dividing by 3.
Volume = (area of base × height) / 3
= (36 cm² × 21 cm) / 3
= 756 cm³ / 3
= 252 cm³
Therefore, the volume of the piece of cheese is 252 cm³.