Question

question 1 (multiple - choice worth 2 points) (06.01 mc) a rectangular pyramid has a height of 5 units and a volume of 50 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 = 10 and h = 5 has a volume of 150 units³, therefore, shannon is correct. b a rectangular prism in which ba = 30 and h = 5 has a volume of 150 units³, therefore, shannon is correct. c a rectangular prism in which ba = 10 and h = 5 has a volume of 50 units³, therefore, shannon is incorrect. d a rectangular prism in which ba = 30 and h = 5 has a volume of 50 units³, therefore, shannon is incorrect.

Explanation:

Step1: Recall volume formulas

Volume of rectangular pyramid $V_p=\frac{1}{3}BA\times h$, volume of rectangular prism $V_r = BA\times h$.

Step2: Calculate pyramid volume

Given $BA = 30$, $h = 5$ for rectangular pyramid. $V_p=\frac{1}{3}\times30\times5= 50$ units³.

Step3: Calculate prism volume

For rectangular prism with same $BA = 30$ and $h = 5$, $V_r=30\times5 = 150$ units³. Prism volume is 3 - times pyramid volume.

Step4: Analyze statements

When $BA = 30$ and $h = 5$, rectangular prism volume is 150 units³ and pyramid volume is 50 units³. Shannon's statement is correct for this case. When $BA = 10$ and $h = 5$, $V_p=\frac{1}{3}\times10\times5=\frac{50}{3}$ units³, $V_r = 10\times5 = 50$ units³, Shannon's statement is incorrect.

Answer:

A rectangular prism in which $BA = 30$ and $h = 5$ has a volume of 150 units³, therefore, Shannon is correct.