Question

question 8 of 10
what is the volume of the cylinder below?
a. 288π units³
b. 378π units³
c. 252π units³
d. 168π units³

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

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

From the figure, the radius \(r = 6\) and the height \(h=7\) (the slant height \(8\) is not used in the volume formula for a cylinder; we use the perpendicular height).

Step3: Substitute the values into the formula

Substitute \(r = 6\) and \(h = 7\) into \(V=\pi r^{2}h\). We get \(V=\pi\times6^{2}\times7\).

Step4: Calculate the value

First, \(6^{2}=36\). Then \(36\times7 = 252\). So \(V = 252\pi\) units\(^3\).

Answer:

C. \(252\pi\) units\(^3\)