A cylinder with height and radius 2:1 is filled with soft drink and then it is titled so as to allow some soft drink to flow off to an extent where the level of soft drink just touches the lowest point of the upper mouth .
If the 2.1 L soft drink is retained in the cylinder , what is the capacity of the cylinder ?

Options

A. 3.6 L
B. 4L
C. 1.2 L
D. 4.2 L

Answer

To solve the problem step by step, we need to understand the relationship between the volume of the cylinder and the amount of soft drink retained after it has been tilted.

### Step 1: Understand the relationship between the volume retained and the total volume of the cylinder.
When the cylinder is tilted, the soft drink level touches the lowest point of the upper mouth. This means that the volume of soft drink retained in the cylinder is half of the total volume of the cylinder.

### Step 2: Set up the equation based on the information given.
Let the total volume of the cylinder be \( V \). According to the problem, the volume of soft drink retained in the cylinder is \( 2.1 \) liters. Since this volume is half of the total volume, we can write the equation:
\[ \frac{V}{2} = 2.1 \text{ liters} \]

### Step 3: Solve for the total volume \( V \).
To find the total volume \( V \), we can multiply both sides of the equation by \( 2 \):
\[ V = 2 \times 2.1 = 4.2 \text{ liters} \]

### Step 4: State the final answer.
The capacity of the cylinder is \( 4.2 \) liters.

### Summary of the solution:
- The volume of soft drink retained is half of the total volume of the cylinder.
- The equation \( \frac{V}{2} = 2.1 \) liters leads us to find that the total volume \( V = 4.2 \) liters.