A medicine-capsule is the shape of a cylinder of diameter `0.5` `cm` with two hemisphere stuck to each of its ends. The length of entire capsule is `2` `cm`. The capacity of the capsule is

Options

A. `0.36 cm^(3)`
B. `0.35 cm^(3)`
C. `0.34 cm^(3)`
D. `0.33 cm^(3)`

Explanation

To find the capacity of the medicine capsule, which consists of a cylindrical part and two hemispherical ends, we will calculate the volume of the cylinder and the volume of the two hemispheres separately, and then sum them up.

### Step-by-Step Solution:

1. **Identify the dimensions of the capsule**:
- Diameter of the cylinder = 0.5 cm
- Radius of the cylinder (r) = Diameter / 2 = 0.5 cm / 2 = 0.25 cm
- Total length of the capsule = 2 cm

2. **Determine the height of the cylindrical part**:
- The capsule has two hemispheres at both ends. The height of each hemisphere is equal to its radius (0.25 cm).
- Therefore, the total height occupied by the two hemispheres = 0.25 cm + 0.25 cm = 0.5 cm.
- Height of the cylindrical part (h) = Total length - Height of two hemispheres = 2 cm - 0.5 cm = 1.5 cm.

3. **Calculate the volume of the cylindrical part**:
- The formula for the volume of a cylinder is given by:
\[ V_{\text{cylinder}} = \pi r^2 h \]
- Substituting the values:
\[ V_{\text{cylinder}} = \pi (0.25)^2 (1.5) = \pi (0.0625) (1.5) = \pi (0.09375) \]

4. **Calculate the volume of one hemisphere**:
- The formula for the volume of a hemisphere is given by:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 \]
- Substituting the radius:
\[ V_{\text{hemisphere}} = \frac{2}{3} \pi (0.25)^3 = \frac{2}{3} \pi (0.015625) = \frac{0.03125}{3} \pi \]

5. **Calculate the volume of two hemispheres**:
- Since there are two hemispheres:
\[ V_{\text{two hemispheres}} = 2 \times V_{\text{hemisphere}} = 2 \times \frac{2}{3} \pi (0.25)^3 = \frac{4}{3} \pi (0.015625) = \frac{0.0625}{3} \pi \]

6. **Total volume of the capsule**:
- Now, add the volume of the cylinder and the volume of the two hemispheres:
\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{two hemispheres}} = \pi (0.09375) + \frac{0.0625}{3} \pi \]

7. **Simplifying the total volume**:
- To combine these, we can factor out \(\pi\):
\[ V_{\text{total}} = \pi \left(0.09375 + \frac{0.0625}{3}\right) \]
- Convert \(0.09375\) to a fraction:
\[ 0.09375 = \frac{15}{160} = \frac{15}{160} + \frac{0.0625}{3} = \frac{15}{160} + \frac{0.0625 \times 53.33}{160} \approx \frac{15 + 0.02083}{160} \]

8. **Final Calculation**:
- Using \(\pi \approx \frac{22}{7}\) for approximation:
\[ V_{\text{total}} \approx \frac{22}{7} \left(0.09375 + 0.02083\right) \approx \frac{22}{7} \times 0.11458 \approx 0.36 \text{ cm}^3 \]

### Conclusion:
The capacity of the capsule is approximately **0.36 cm³**.