Question

1. if a cone has a volume of 300π cm³ and a height of 15 cm, what is the radius of the base?

a. 6 cm
b. 7 cm
c. 4√5 cm
d. 2√15 cm

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 \(V\) is the volume, \(r\) is the radius of the base, and \(h\) is the height.

Step2: Substitute the given values into the formula

We are given \(V = 300\pi\space cm^{3}\) and \(h=15\space cm\). Substituting these into the formula gives \(300\pi=\frac{1}{3}\pi r^{2}(15)\).

Step3: Simplify the equation

First, cancel out \(\pi\) from both sides of the equation. We get \(300=\frac{1}{3}(15)r^{2}\). Then, \(\frac{1}{3}(15) = 5\), so the equation becomes \(300 = 5r^{2}\).

Step4: Solve for \(r^{2}\)

Divide both sides of the equation \(300 = 5r^{2}\) by \(5\). We have \(r^{2}=\frac{300}{5}=60\).

Step5: Solve for \(r\)

Take the square root of both sides. \(r=\sqrt{60}\). Simplify \(\sqrt{60}=\sqrt{4\times15}=2\sqrt{15}\space cm\).

Answer:

d. \(2\sqrt{15}\space cm\)