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 rectangular prism in which ba = 12 and h = 5 has a volume of 60 units³; therefore, shannon is incorrect. 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 180 units³; therefore, shannon is correct. a rectangular prism in which ba = 36 and h = 5 has a volume of 180 units³; therefore, shannon is correct.

Explanation:

Step1: Recall volume formulas

The volume formula for a rectangular - prism is $V = BA\times h$, where $BA$ is the base - area and $h$ is the height. The volume formula for a rectangular pyramid is $V=\frac{1}{3}BA\times h$.

Step2: Given the volume of the pyramid

Given that the volume of the rectangular pyramid $V_p = 60$ units³ and $h = 5$ units. Using the pyramid volume formula $V_p=\frac{1}{3}BA\times h$, we can find the base - area. Substitute the values into the formula: $60=\frac{1}{3}BA\times5$. Solving for $BA$, we get $BA=\frac{60\times3}{5}=36$ square units.

Step3: Calculate the volume of the prism with the same base - area and height

For a rectangular prism with the same base - area $BA = 36$ square units and height $h = 5$ units, using the prism volume formula $V = BA\times h$, we have $V=36\times5 = 180$ units³.

Answer:

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