Find the capacity of a cyclinder container with internal diameter 28 cm and height 20 cm.

Answer

To find the capacity of a cylindrical container, we need to calculate the volume of the cylinder using the given dimensions. Here’s a step-by-step solution:

### Step 1: Identify the given dimensions
- Internal diameter of the cylinder = 28 cm
- Height of the cylinder = 20 cm

### Step 2: Calculate the radius of the cylinder
The radius (r) is half of the diameter.
\[ r = \frac{\text{diameter}}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm} \]

### Step 3: Use the formula for the volume of a cylinder
The formula for the volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately \( 3.14 \) or \( \frac{22}{7} \).

### Step 4: Substitute the values into the formula
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times (14 \text{ cm})^2 \times 20 \text{ cm} \]

### Step 5: Calculate \( r^2 \)
\[ (14 \text{ cm})^2 = 196 \text{ cm}^2 \]

### Step 6: Substitute \( r^2 \) back into the volume formula
\[ V = \frac{22}{7} \times 196 \text{ cm}^2 \times 20 \text{ cm} \]

### Step 7: Calculate the volume
First, calculate \( 196 \times 20 \):
\[ 196 \times 20 = 3920 \text{ cm}^3 \]

Now substitute this back into the volume formula:
\[ V = \frac{22}{7} \times 3920 \text{ cm}^3 \]

### Step 8: Simplify the calculation
\[ V = 22 \times 560 \text{ cm}^3 \quad \text{(since } \frac{3920}{7} = 560\text{)} \]

### Step 9: Final calculation
\[ V = 12320 \text{ cm}^3 \]

### Conclusion
The capacity of the cylindrical container is \( 12320 \text{ cm}^3 \).

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