Question

question 6 of 25
what is the volume of a cone with a radius of 4 and a height of 15?
a. 900 units³
b. 39.79 units³
c. 753.98 units³
d. 251.33 units³

Explanation:

Step1: Recall the volume formula for 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: Substitute the given values into the formula

Given \(r = 4\) and \(h=15\), we substitute these into the formula: \(V=\frac{1}{3}\times\pi\times4^{2}\times15\).
First, calculate \(4^{2}=16\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times16\times15\).
Since \(\frac{1}{3}\times15 = 5\), the formula simplifies to \(V = 5\times16\times\pi\).
\(5\times16=80\), so \(V = 80\pi\).

Step3: Calculate the numerical value

Taking \(\pi\approx3.1416\), we have \(V=80\times3.1416 = 251.328\approx251.33\) units\(^{3}\).

Answer:

D. \(251.33\) units\(^{3}\)