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.

Question

Mathematics

Joseph Blackwell

21 May, 20:54

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.

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Danica Church · Answer 1

Question

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

b) A rectangular prism in which BA = 12 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

c) A rectangular prism in which BA = 36 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

d) A rectangular prism in which BA = 12 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

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:

The formula for the volume of a Rectangular Pyramid = 1/3 * Base Area * Height

In the question,

Base Area = ?

Height = 5 units

Volume = 60 units³

So,

60 = 1/3 * BA * 5

Cross Multiply

180 = 5BA

BA = 180/5

BA = 36 units²

Also, the Volume of a Rectangular Prism =

Base Area * Height

From the above question

Base Area = 36 units²

Height = 5 units

Volume of the Rectangular prism = 36 units² * 5 units

= 180 units³

Therefore, the statement that explains whether Shannon is correct is option a,

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