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A rectangular pyramid has a height of 5 units and a volume of 60 units3. 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 rectangular prism in which BA = 36 and h = 5 has a volume of 180 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 12 and h = 5 has a volume of 180 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 36 and h = 5 has a volume of 60 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 12 and h = 5 has a volume of 60 units3; therefore, Shannon is incorrect.

Sagot :

Murphyamber2002

Answer:

A. A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units3; therefore, Shannon is correct.

Step-by-step explanation:

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akposevictor

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.

Learn more about volume of rectangular pyramid on:

https://brainly.com/question/924442

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