Question

what is the formula for the volume of a cylinder?
a. $\pi rh^{2}$
b. $\pi r^{2}h$
c. $2\pi rh$
d. $\frac{1}{3}\pi r^{2}h$

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \(V\) of a cylinder is given by the product of the area of the base and the height.

Step2: Find the area of the base

The base of a cylinder is a circle. The area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the base.

Step3: Multiply by the height

Let \(h\) be the height of the cylinder. Then \(V=A\times h=\pi r^{2}h\).

• Option A: \(\pi rh^{2}\) is incorrect as the formula for the volume of a cylinder has \(r^{2}\) (from the area of the circular base) not \(h^{2}\).
• Option C: \(2\pi rh\) is the formula for the lateral (curved) surface area of a cylinder, not the volume.
• Option D: \(\frac{1}{3}\pi r^{2}h\) is the formula for the volume of a cone.

Answer:

B. $\pi r^{2}h$