Question

1. if a cone has a volume of \\( \frac { 250 } { 3 } \pi \mathrm { cm } ^ { 3 } \\) and a height of 10 cm, what is the radius of the base?

a. 6 cm
b. 5 cm
c. 3 cm
d. 4 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 that \(V = \frac{250}{3}\pi\space cm^{3}\) and \(h=10\space cm\). Substituting these into the formula \(\frac{250}{3}\pi=\frac{1}{3}\pi r^{2}(10)\).

Step3: Simplify the equation

First, cancel out the \(\frac{1}{3}\pi\) on both sides of the equation. We get \(250 = 10r^{2}\).

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

Divide both sides of the equation \(250 = 10r^{2}\) by \(10\). So, \(r^{2}=\frac{250}{10}=25\).

Step5: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r = \sqrt{25}=5\space cm\).

Answer:

B. 5 cm