Question

if a cylinder has a radius of 4 units and a height of 8 units, what is its volume in terms of \\( \pi \\)?
a. \\( v = 128\pi \\) cubic units
b. \\( v = 32\pi \\) cubic units
c. \\( v = 96\pi \\) cubic units
d. \\( v = 64\pi \\) cubic units

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume 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 \(r = 4\) and \(h=8\). First, calculate \(r^{2}\): \(r^{2}=4^{2}=16\). Then, multiply by \(h\) and \(\pi\): \(V=\pi\times16\times8\).

Step3: Perform the multiplication

\(16\times8 = 128\), so \(V = 128\pi\).

Answer:

A. \(V = 128\pi\) cubic units