A rectangular pyramid has a height of 5 units and a volume of 50 units^3. 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 = 10 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.

A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.

A rectangular prism in which BA = 10 and h = 5 has a volume of 50 units^3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 30 and h = 5 has a volume of 50 units^3; therefore, Shannon is incorrect.

[tex]\text{The formula of a volume of a pyraimid:}\\\\V=\dfrac{1}{3}BH\\\\B-base\ area\\H-height\\\\\text{We have}\ H=5\ \text{and}\ V=50.\ \text{Substitute and calculate thw base area:}\\\\50=\dfrac{1}{3}B(5)\qquad\text{multiply both sides by 3}\\\\150=5B\qquad\text{divide both sides by 5}\\\\30=B\to B=30\ units^2[/tex]

[tex]\text{The formula of a volume of a prism:}\\\\V=BH\\\\B-base\ area\\H-height\\\\\text{We have}\ B=30\ \text{and}\ H=5.\ \text{Substitute:}\\\\V=(30)(5)=150\ units^3[/tex]

psm22415 psm22415 · Answer 2 · 2022-01-31T07:07:31+01:00

The volume of the rectangular pyramid is defined as the capacity of the rectangular pyramid.

A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.

Given

The height of the rectangular pyramid = 5 units

The volume of the rectangular pyramid = 50 cubic units

What is a rectangular pyramid?

The volume of the rectangular pyramid is defined as the capacity of the rectangular pyramid.

The formula of the rectangular pyramid is given by;

[tex]\rm Volume \ of \ rectangular \ pyramid = \dfrac{1}{3} \times Base \times Height[/tex]

The base of the pyramid is BA.

Substitute all the values in the formula;

[tex]\rm Volume \ of \ rectangular \ pyramid = \dfrac{1}{3} \times Base \times Height\\\\\rm 50 = \dfrac{1}{3} \times BA \times 5\\\\BA = \dfrac{50\times 3}{5}\\\\BA = 10 \times 3\\\\BA = 30[/tex]

The volume of the prism is given by;

[tex]\rm Volume \ of \ prism= Base \times Height\\\\Volume \ of \ prism= 30 \times 5\\\\Volume \ of \ prism= 150 \ units ^3[/tex]

Hence, A rectangular prism in which BA = 30 and h = 5 has a volume of 150 units^3; therefore, Shannon is correct.

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