Find the volume of the sphere whose diameter is :
(a) 7 cm
(b ) 1 cm

Answer

To find the volume of a sphere given its diameter, we can use the formula for the volume of a sphere:

\[ V = \frac{4}{3} \pi r^3 \]

where \( r \) is the radius of the sphere.

### Step-by-Step Solution

#### Part (a): Diameter = 7 cm

1. **Find the radius**:
\[ r = \frac{\text{diameter}}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

2. **Calculate the volume**:
\[ V = \frac{4}{3} \pi r^3 \]
Substitute \( r = 3.5 \text{ cm} \):
\[ V = \frac{4}{3} \pi (3.5)^3 \]

3. **Calculate \( (3.5)^3 \)**:
\[ (3.5)^3 = 3.5 \times 3.5 \times 3.5 = 42.875 \]

4. **Substitute back into the volume formula**:
\[ V = \frac{4}{3} \pi (42.875) \]

5. **Use \( \pi \approx \frac{22}{7} \)**:
\[ V = \frac{4}{3} \times \frac{22}{7} \times 42.875 \]

6. **Calculate the volume**:
\[ V = \frac{4 \times 22 \times 42.875}{3 \times 7} \]
\[ V = \frac{4 \times 22 \times 42.875}{21} \]
\[ V \approx \frac{4 \times 22 \times 42.875}{21} \approx 179.66 \text{ cm}^3 \]

#### Part (b): Diameter = 1 cm

1. **Find the radius**:
\[ r = \frac{\text{diameter}}{2} = \frac{1 \text{ cm}}{2} = 0.5 \text{ cm} \]

2. **Calculate the volume**:
\[ V = \frac{4}{3} \pi r^3 \]
Substitute \( r = 0.5 \text{ cm} \):
\[ V = \frac{4}{3} \pi (0.5)^3 \]

3. **Calculate \( (0.5)^3 \)**:
\[ (0.5)^3 = 0.5 \times 0.5 \times 0.5 = 0.125 \]

4. **Substitute back into the volume formula**:
\[ V = \frac{4}{3} \pi (0.125) \]

5. **Use \( \pi \approx \frac{22}{7} \)**:
\[ V = \frac{4}{3} \times \frac{22}{7} \times 0.125 \]

6. **Calculate the volume**:
\[ V = \frac{4 \times 22 \times 0.125}{3 \times 7} \]
\[ V = \frac{11}{21} \approx 0.52 \text{ cm}^3 \]

### Final Answers:
- (a) Volume of the sphere with diameter 7 cm is approximately **179.66 cm³**.
- (b) Volume of the sphere with diameter 1 cm is approximately **0.52 cm³**.