Question

1. a cone has a radius of 2 units and a height of 4 units. what is its volume?

a. 8.37 cubic units
b. 12.56 cubic units
c. 16.75 cubic units
d. 25.12 cubic units

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: Substitute the given values into the formula

Given \(r = 2\) units and \(h=4\) units. Substitute into \(V=\frac{1}{3}\pi r^{2}h\):
\(V=\frac{1}{3}\times\pi\times(2)^{2}\times4\)
First, calculate \((2)^{2}=4\). Then the expression becomes \(V=\frac{1}{3}\times\pi\times4\times 4=\frac{16\pi}{3}\)

Step3: Calculate the numerical value

Take \(\pi\approx3.14\). Then \(V=\frac{16\times3.14}{3}=\frac{50.24}{3}\approx16.75\)

Answer:

C. 16.75 cubic units