Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

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

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