The statement that explains whether Shannon is correct about the volumes of a rectangular prism and pyramid is: a. A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units3; therefore, Shannon is correct.
What is the Volume of a Rectangular Pyramid?
A rectangular prism has the following volume formula, l × w × h, where l × w is the base area and h is the height of the rectangular prism.
The volume formula for a rectangular pyramid = 1/3(l × w × h).
This means that the volume of a rectangular prism, l × w × h, would be 3 times the volume of a rectangular pyramid, 1/3(l × w × h), if they both have the same base and height.
Given the dimensions of a rectangular pyramid as:
Height = 5 units
Volume = 60 units³
60 = 1/3(BA × 5)
180 = 5BA
BA = 180/5
BA = 36 units²
Volume of the rectangular prism with same BA (36) and height (5) would be:
Volume of rectangular prism = 36 × 5 = 180 units³
Therefore, the statement that explains whether Shannon is correct about the volumes of a rectangular prism and pyramid is: a. A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units3; therefore, Shannon is correct.
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