Question

find the value of x.

1. v = 64 in³
2. v = 147π cm³
3. v = 56 m³
4. multiple choice a right cone has a height of 6 feet and a volume of 32π cubic feet. what is its radius?

a. 2 ft
b. 3 ft
c. 4 ft
d. 5 ft
find the volume of the solid. the prisms, pyramids, and cones are right. round your answer to the hundredths place.
11.
12.

Explanation:

Step 1: 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.

Step 2: Substitute the given values into the formula

We are given that $V = 32\pi$ cubic - feet and $h=6$ feet. Substituting these values into the formula $V=\frac{1}{3}\pi r^{2}h$, we get $32\pi=\frac{1}{3}\pi r^{2}\times6$.

Step 3: Simplify the equation

First, simplify the right - hand side of the equation: $\frac{1}{3}\pi r^{2}\times6 = 2\pi r^{2}$. So our equation becomes $32\pi=2\pi r^{2}$.

Step 4: Solve for $r^{2}$

Divide both sides of the equation $32\pi=2\pi r^{2}$ by $2\pi$. Since $\frac{32\pi}{2\pi}=\frac{2\pi r^{2}}{2\pi}$, we have $r^{2}=16$.

Step 5: Solve for $r$

Take the square root of both sides. Since $r>0$ (as it represents a radius), $r = 4$ feet.

Answer:

C. 4 ft