Find the volume of the sphere whose radius is :
(a) 2 cm
(b) 3 cm
(c ) 1 cm

Answer

To find the volume of a sphere given its radius, we use the formula:

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

where \( V \) is the volume and \( r \) is the radius of the sphere.

Let's solve the problem step by step for each given radius.

### (a) Radius = 2 cm

1. **Identify the radius**:
\[ r = 2 \, \text{cm} \]

2. **Substitute the radius into the volume formula**:
\[ V = \frac{4}{3} \pi (2)^3 \]

3. **Calculate \( r^3 \)**:
\[ (2)^3 = 8 \]

4. **Substitute back into the formula**:
\[ V = \frac{4}{3} \pi \times 8 \]

5. **Multiply**:
\[ V = \frac{32}{3} \pi \, \text{cm}^3 \]

### (b) Radius = 3 cm

1. **Identify the radius**:
\[ r = 3 \, \text{cm} \]

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

3. **Calculate \( r^3 \)**:
\[ (3)^3 = 27 \]

4. **Substitute back into the formula**:
\[ V = \frac{4}{3} \pi \times 27 \]

5. **Multiply**:
\[ V = \frac{108}{3} \pi \]
\[ V = 36 \pi \, \text{cm}^3 \]

### (c) Radius = 1 cm

1. **Identify the radius**:
\[ r = 1 \, \text{cm} \]

2. **Substitute the radius into the volume formula**:
\[ V = \frac{4}{3} \pi (1)^3 \]

3. **Calculate \( r^3 \)**:
\[ (1)^3 = 1 \]

4. **Substitute back into the formula**:
\[ V = \frac{4}{3} \pi \times 1 \]

5. **Final volume**:
\[ V = \frac{4}{3} \pi \, \text{cm}^3 \]

### Summary of Volumes
- For radius 2 cm: \( V = \frac{32}{3} \pi \, \text{cm}^3 \)
- For radius 3 cm: \( V = 36 \pi \, \text{cm}^3 \)
- For radius 1 cm: \( V = \frac{4}{3} \pi \, \text{cm}^3 \)