f r is the radius of the​ hemisphere, h the height of the​ cylinder, and V the​ volume, then 

requals=enter your response here 

and 

hequals=enter your response here.

​(Type exact​ answers, using 

piπ 

as​ needed.)

Let's express \( r \) and \( h \) using the given total volume \( V \).

### Volume Equation:
The total volume of the silo consists of the volume of the cylinder and the volume of the hemisphere:

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

### Step 1: Express \( h \) in terms of \( V \) and \( r \)

To solve for \( h \), isolate \( h \) in the equation above:

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

Thus, \( h \) is

f r is the radius of the hemisphere, h the height of the cylinder, and V the volume, then r equals=enter your response here and h equals=enter your response here. (Type exact answers, using piπ as needed.)

This problem explores how to express the radius (r) and height (h) of a silo, consisting of a cylinder and a hemisphere, given the total volume (V). The solution involves geometric formulas for the volume of a cylinder and a hemisphere, and algebraic manipulation to isolate h in terms of V and r. Suitable for high school geometry students.

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