Question

what is the volume of the cone below?
a. 56π units³
b. 168π units³
c. 336π units³
d. 112π units³

Explanation:

Step1: Recall the formula for the volume of a cone

The volume formula for a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

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

From the problem, \(r = 4\) and \(h=21\).

Step3: Substitute the values into the formula

Substitute \(r = 4\) and \(h = 21\) into \(V=\frac{1}{3}\pi r^{2}h\):

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Step4: Simplify the expression

First, calculate \(\frac{1}{3}\times16\times21\). \(\frac{1}{3}\times21 = 7\), then \(7\times16=112\). So \(V = 112\pi\) units\(^{3}\).

Answer:

D. \(112\pi\) units\(^{3}\)