Question

what is the formula for the volume of a cylinder?
a. $\frac{4}{3}\pi r^{2}h$
b. $\frac{4}{3}\pi r^{3}$
c. $\pi r^{3}$
d. $\pi r^{2}h$

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. The base of a cylinder is a circle with area \(A = \pi r^{2}\), and the height is \(h\). So \(V=\text{Base Area}\times\text{Height}\).

Step2: Substitute the base - area formula into the volume formula

Substituting \(A=\pi r^{2}\) into \(V = A\times h\), we get \(V=\pi r^{2}h\).

Now let's check the options:

• Option a: \(\frac{4}{3}\pi r^{2}h\) is not the formula for the volume of a cylinder.
• Option b: \(\frac{4}{3}\pi r^{3}\) is the formula for the volume of a sphere.
• Option c: \(\pi r^{3}\) is not a standard formula for common 3 - D shapes.
• Option d: \(\pi r^{2}h\) is the formula for the volume of a cylinder.

Answer:

d. \(\pi r^{2}h\)