Question

A rectangular pyramid has a height of 6 units and a volume of 40 units. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

A) Shannon is correct because the volume of a rectangular prism is always three times the volume of a rectangular pyramid.
B) Shannon is incorrect because the volume of a rectangular prism with the same base area and height is eight times the volume of the given rectangular pyramid.
C) Shannon is correct because the volume of a rectangular prism with the same base area and height is three times the volume of the given rectangular pyramid.
D) Shannon is incorrect because the volume of a rectangular prism is always half the volume of a rectangular pyramid.

Answer 1

Shannon is incorrect because the volume of the rectangular prism is six times the size of the given rectangular pyramid, not three times.

Step-by-step explanation:

To determine whether Shannon is correct, we need to compare the volumes of the rectangular pyramid and the rectangular prism. The volume of a rectangular pyramid is given by 1/3 times the base area times the height. Since the volume of the pyramid is 40 units and the height is 6 units, we can find the base area by dividing the volume by 1/3 times the height. This gives us a base area of 40 / (1/3 * 6) = 20 units.

Now, let's calculate the volume of the rectangular prism. The volume of a rectangular prism is given by the base area times the height. Since the base area is 20 units and the height is 6 units, the volume of the prism is 20 * 6 = 120 units. Therefore, Shannon is incorrect because the volume of the rectangular prism is six times the size of the given rectangular pyramid, not three times.