Question

a cylinder has a volume of $117\\ cm^3$. what is the volume of a cone with the same radius and height? (show your work for credit)
\bigcirc $26\\ cm^3$
\bigcirc $39\\ cm^3$
\bigcirc $156\\ cm^3$
\bigcirc $234\\ cm^3$

Explanation:

Step1: Recall volume formulas

Volume of cylinder: $V_{cyl} = \pi r^2 h$
Volume of cone: $V_{cone} = \frac{1}{3} \pi r^2 h$

Step2: Relate cone to cylinder volume

Since $V_{cyl} = \pi r^2 h = 117\ \text{cm}^3$, substitute into cone formula:
$V_{cone} = \frac{1}{3} V_{cyl}$

Step3: Calculate cone volume

$V_{cone} = \frac{1}{3} \times 117$

Answer:

B. $39\ \text{cm}^3$