Question

1. a cylinder has a volume of 78 cubic centimeters. what is the volume of a cone with the same radius and height?

a. 26 cubic centimeters
b. 39 cubic centimeters
c. 156 cubic centimeters
d. 234 cubic centimeters
v = 78 cu. cm
v = ?

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 and cylinder volumes

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

Step3: Calculate cone volume

Substitute $V_{cyl}=78$: $V_{cone} = \frac{1}{3} \times 78 = 26$

Answer:

A. 26 cubic centimeters