An oil tank has the shape of a right circular cylinder is 12 centimeters in height and has a volume of 108`pi` cubic centimeters. What is the diameter of the base of the cylinder, in centimeters?

Answer

To find the diameter of the base of the cylinder, we can follow these steps:

### Step 1: Write down the formula for the volume of a cylinder.
The volume \( V \) of a right circular cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.

### Step 2: Substitute the known values into the formula.
We know the volume \( V = 108\pi \) cubic centimeters and the height \( h = 12 \) centimeters. Substituting these values into the formula gives:
\[ 108\pi = \pi r^2 \cdot 12 \]

### Step 3: Simplify the equation.
We can cancel \( \pi \) from both sides of the equation:
\[ 108 = r^2 \cdot 12 \]

### Step 4: Solve for \( r^2 \).
Next, we divide both sides by 12 to isolate \( r^2 \):
\[ r^2 = \frac{108}{12} \]
Calculating the right side gives:
\[ r^2 = 9 \]

### Step 5: Solve for \( r \).
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{9} = 3 \]

### Step 6: Calculate the diameter.
The diameter \( d \) of the cylinder is twice the radius:
\[ d = 2r = 2 \times 3 = 6 \]

### Final Answer:
The diameter of the base of the cylinder is \( 6 \) centimeters.

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