A cylinder has a radius of 3 cm and a height of 8 cm. What is its volume expressed in terms of π?

• A. 60 cmπ³
• B. 72 cmπ³
• C. 80 cmπ³
• D. 90 cmπ³

Answer: (B)

To determine the volume of a cylinder, the formula used is:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius, and ( h ) is the height of the cylinder.

In this case, the radius ( r ) is 3 cm and the height ( h ) is 8 cm. We can substitute these values into the formula:

1. Calculate ( r^2 ):

[ r^2 = 3^2 = 9 ]

2. Multiply ( r^2 ) by ( h ):

[ r^2 h = 9 \times 8 = 72 ]

3. Finally, multiply by ( \pi ):

[ V = \pi \times 72 = 72\pi \text{ cm}^3 ]

Thus, the volume of the cylinder is ( 72 \text{ cm}^3\pi ).

This calculation confirms that the volume expressed in terms of ( \pi ) is indeed ( 72 \text{ cm}^3\pi ), making it the correct choice.