A cone has a volume of 100π cubic inches. If the height of the cone is 12 inches, then what is the radius of the cone?(1 point)

The radius of the cone is
inches.

1 answer

The volume \( V \) of a cone is given by the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height.

In this case, we know that:

\[ V = 100\pi \quad \text{and} \quad h = 12 \]

Substituting these values into the volume formula:

\[ 100\pi = \frac{1}{3} \pi r^2 (12) \]

We can simplify this equation. First, cancel \( \pi \) from both sides:

\[ 100 = \frac{1}{3} r^2 (12) \]

Next, simplify \( \frac{1}{3} (12) \):

\[ 100 = 4r^2 \]

Now, solve for \( r^2 \):

\[ r^2 = \frac{100}{4} = 25 \]

Taking the square root of both sides gives:

\[ r = \sqrt{25} = 5 \]

Thus, the radius of the cone is

\[ \boxed{5} \text{ inches.} \]