Question

question 4 of 10
what is the volume of the cylinder below?

a. 84 units³
b. 96π units³
c. 168π units³
d. 112π units³

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Identify the values of \(r\) and \(h\)

From the figure, the radius \(r = 4\) and the height \(h=6\) (the perpendicular height is used for volume calculation, not the slant height).

Step3: Substitute the values into the formula

Substitute \(r = 4\) and \(h = 6\) into \(V=\pi r^{2}h\).
We get \(V=\pi\times4^{2}\times6\).
First, calculate \(4^{2}=16\).
Then \(V=\pi\times16\times6\).
Since \(16\times6 = 96\), so \(V = 96\pi\) units\(^3\).

Answer:

B. \(96\pi\) units\(^3\)