Find the volume of a cylinder with a radius of 3 cm and a height of 5 cm.

To find the volume of a cylinder, you can use the formula:

[ 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 is 3 cm and the height is 5 cm.

1. First, calculate the area of the base of the cylinder, which is a circle:

[ \text{Area} = \pi r^2 = \pi (3)^2 = \pi \cdot 9 = 9\pi ]

2. Next, multiply the area of the base by the height to find the volume:

[ V = \text{Area} \cdot h = 9\pi \cdot 5 = 45\pi ]

Thus, the volume of the cylinder is ( 45\pi ) cm³. This computation shows that taking both the radius and height into account correctly applies the formula, leading to the conclusion that option B is the correct answer.