Question

1. a conical silo has a volume of 500πm³ and a radius of 5 m. what is the height of the silo?

a. 42 m
b. 55 m
c. 60 m
d. 30 m

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, and \(h\) is the height.

Step2: Substitute the given values into the formula

We know that \(V = 500\pi\) and \(r = 5\). Substituting these into the formula gives \(500\pi=\frac{1}{3}\pi(5)^{2}h\).

Step3: Simplify the equation

First, cancel out \(\pi\) from both sides of the equation: \(500=\frac{1}{3}(25)h\). Then, multiply both sides by \(3\) to get \(1500 = 25h\).

Step4: Solve for \(h\)

Divide both sides by \(25\): \(h=\frac{1500}{25}=60\).

Answer:

C. 60 m