Question

1. a cone has a radius of 6 cm and a volume of 72π cm³. what is the height of the cone?

a. 8 cm
b. 4 cm
c. 2 cm
d. 6 cm

Explanation:

Step1: Recall the volume formula of a cone

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

Step2: Substitute the given values into the formula

We are given that \(V = 72\pi\space cm^{3}\) and \(r = 6\space cm\). Substituting these into the formula \(V=\frac{1}{3}\pi r^{2}h\), we get \(72\pi=\frac{1}{3}\pi\times(6)^{2}\times h\).

Step3: Simplify the equation

First, simplify \(\frac{1}{3}\pi\times(6)^{2}\times h\). \(\frac{1}{3}\times36\pi\times h = 12\pi h\). So the equation becomes \(72\pi=12\pi h\).

Step4: Solve for \(h\)

Divide both sides of the equation \(72\pi = 12\pi h\) by \(12\pi\). \(\frac{72\pi}{12\pi}=h\). Since \(\frac{72}{12}=6\), we find that \(h = 6\space cm\).

Answer:

d. \(6\space cm\)