Question

what is the volume of the cone below?
a. 5112π units³
b. 3408π units³
c. 852π units³
d. 10,224π units³

Explanation:

Step1: Recall the formula for the volume of a cone

The volume formula of 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, \(r = 12\) and \(h=71\).

Step3: Substitute the values into the formula

Substitute \(r = 12\) and \(h = 71\) into \(V=\frac{1}{3}\pi r^{2}h\).
First, calculate \(r^{2}\): \(r^{2}=12^{2}=144\).
Then, calculate \(\frac{1}{3}\times r^{2}\times h\): \(\frac{1}{3}\times144\times71 = 48\times71=3408\).
Finally, \(V=\frac{1}{3}\pi\times12^{2}\times71=\pi\times48\times71 = 852\pi\).

Answer:

C. \(852\pi\) units\(^{3}\)