The circumference of the base of a circular cylinder is `8pi` cm. The height of the cylinder is same as the diameter of the base. How much water can the cylinder hold?

Options

A. `128 pi` litres
B. `0.128 pi` litres
C. `630 pi` litres
D. `0.164 pi` litres

Answer

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

### Step 1: Understand the Given Information
The circumference of the base of the circular cylinder is given as \( 8\pi \) cm. The height of the cylinder is the same as the diameter of the base.

### Step 2: Use the Circumference Formula
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
We can set up the equation using the given circumference:
\[ 2\pi r = 8\pi \]

### Step 4: Simplify the Equation
To find \( r \), we can divide both sides of the equation by \( 2\pi \):
\[ r = \frac{8\pi}{2\pi} = 4 \text{ cm} \]

### Step 5: Calculate the Diameter
The diameter \( d \) of the base is twice the radius:
\[ d = 2r = 2 \times 4 = 8 \text{ cm} \]

### Step 6: Determine the Height of the Cylinder
According to the problem, the height \( h \) of the cylinder is the same as the diameter:
\[ h = d = 8 \text{ cm} \]

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

### Step 8: Substitute the Values
Now, substitute \( r = 4 \) cm and \( h = 8 \) cm into the volume formula:
\[ V = \pi (4)^2 (8) \]

### Step 9: Calculate the Volume
Calculating the volume:
\[ V = \pi (16)(8) = 128\pi \text{ cm}^3 \]

### Step 10: Conclusion
The cylinder can hold \( 128\pi \) cubic centimeters of water.

---