Question

a cone has a volume of $150\pi\mathrm{cm}^{3}$ and a radius of 5 cm. what is the height?
a. 18 cm
b. 20 cm
c. 15 cm
d. 12 cm

Explanation:

Step1: Write the formula for the volume 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

Given \(V = 150\pi\space cm^{3}\) and \(r = 5\space cm\). Substituting into \(V=\frac{1}{3}\pi r^{2}h\), we get \(150\pi=\frac{1}{3}\pi\times(5)^{2}\times h\).

Step3: Simplify the equation

First, cancel out \(\pi\) on both sides of the equation. The equation becomes \(150=\frac{1}{3}\times25\times h\). Then, \(\frac{25}{3}h=150\).

Step4: Solve for \(h\)

Multiply both sides of the equation by \(\frac{3}{25}\). So \(h = 150\times\frac{3}{25}\). Calculate \(150\div25 = 6\), then \(6\times3=18\). So \(h = 18\space cm\).

Answer:

A. 18 cm