If a cylinder has a base radius of 3 and a height of 5, what is its volume in terms of pi?

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

[

V = \pi r^2 h

]

Where ( V ) represents the volume, ( r ) is the radius of the base, and ( h ) is the height.

In this case, the base radius is given as 3 and the height is 5. Plugging in these values into the formula gives:

[

V = \pi (3)^2 (5)

]

Calculating ( (3)^2 ) results in 9. Thus, the equation transforms into:

[

V = \pi (9) (5)

]

Now, multiplying 9 by 5 gives you 45. Therefore, we have:

[

V = 45\pi

]

This calculation means the correct volume of the cylinder is 45π. The justified solution leads to the correct answer being thoroughly understood as the multiplication and substitution process aligned with the geometric principles of a cylinder's volume.