Question

a cylinder has a radius of 3 cm and a height of 8 cm. what is the volume of the cylinder in terms of π?
a. 72π cm³
b. 24π cm³
c. 18π cm³
d. 54π cm³

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume \(V\) of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 3\mathrm{cm}\) and \(h=8\mathrm{cm}\). Substitute these values into the formula: \(V=\pi\times(3)^{2}\times8\).

Step3: Simplify the expression

First, calculate \((3)^{2}=9\). Then, \(V=\pi\times9\times8\). Multiply \(9\times8 = 72\). So, \(V = 72\pi\mathrm{cm}^3\).

Answer:

A. \(72\pi\mathrm{cm}^3\)