Question

the volume of the cone is 192π m³. the height of the cone is 9 m. what is the radius of the base of the cone? a 32 m b 24 m c 16 m d 8 m

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step2: Substitute given values

We know that $V = 192\pi$ and $h=9$. Substituting into the formula gives $192\pi=\frac{1}{3}\pi r^{2}\times9$.

Step3: Simplify the equation

First, simplify the right - hand side. $\frac{1}{3}\times9 = 3$, so the equation becomes $192\pi=3\pi r^{2}$. Divide both sides of the equation by $3\pi$. $\frac{192\pi}{3\pi}=r^{2}$, which simplifies to $r^{2}=64$.

Step4: Solve for r

Take the square root of both sides. Since $r$ represents a radius (a non - negative quantity), $r = 8$ (we ignore the negative root $r=-8$ as radius cannot be negative).

Answer:

D. 8 m