The circumference of the base of a circular cylinder is 6`pi` cm. The height of the cylinder equal to the diameter of the base. How many litres of water can it hold?

Options

A. `54 pi`
B. `36 pi`
C. `0.054 pi `
D. `0.54 pi`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
We know that the circumference of the base of the circular cylinder is \(6\pi\) cm. The height of the cylinder is equal to the diameter of the base.

### Step 2: Use the formula for circumference
The formula for the circumference \(C\) of a circle is given by:
\[ C = 2\pi r \]
where \(r\) is the radius of the base.

### Step 3: Set up the equation
Given that the circumference is \(6\pi\) cm, we can set up the equation:
\[ 2\pi r = 6\pi \]

### Step 4: Solve for the radius \(r\)
To find \(r\), we can divide both sides of the equation by \(2\pi\):
\[ r = \frac{6\pi}{2\pi} = \frac{6}{2} = 3 \text{ cm} \]

### Step 5: Find the diameter of the base
The diameter \(d\) of the base is twice the radius:
\[ d = 2r = 2 \times 3 = 6 \text{ cm} \]

### Step 6: Determine the height of the cylinder
According to the problem, the height \(h\) of the cylinder is equal to the diameter of the base:
\[ h = d = 6 \text{ cm} \]

### Step 7: Use the formula for the volume of a cylinder
The volume \(V\) of a cylinder is given by:
\[ V = \pi r^2 h \]

### Step 8: Substitute the values into the volume formula
Now we can substitute \(r = 3\) cm and \(h = 6\) cm into the formula:
\[ V = \pi (3)^2 (6) = \pi (9)(6) = 54\pi \text{ cm}^3 \]

### Step 9: Convert cubic centimeters to liters
Since \(1 \text{ liter} = 1000 \text{ cm}^3\), we can convert the volume from cubic centimeters to liters:
\[ V = \frac{54\pi \text{ cm}^3}{1000} \text{ liters} \]

### Final Answer
The volume of water the cylinder can hold is \(54\pi \text{ cm}^3\) or approximately \(0.1697\pi\) liters.

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