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The image appears to contain handwritten mathematical content, with a particular focus on a sphere with a radius of 4 cm. Let's analyze the relevant information.

### Given:
- **Sphere with radius \( r = 4 \) cm**

### Common Calculations for a Sphere:
1. **Volume of the Sphere**:
   \[
   V = \frac{4}{3} \pi r^3
   \]
2. **Surface Area of the Sphere**:
   \[
   A = 4 \pi r^2
   \]

### Let's calculate the volume and surface area using \( r = 4 \) cm:

1. **Volume**:
   \[
   V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi \times 64 = \frac{256}{3} \pi \approx 268.08 \, \text{cm}^3
   \]

2. **Surface Area**:
   \[
   A = 4 \pi (4)^2 = 4 \pi \times 16 = 64 \pi \approx 201.06 \, \text{cm}^2
   \]

These are the calculated volume and surface area of the sphere.

Would you like a more detailed explanation of these formulas or any other assistance? 

### Related Questions:
1. How do you derive the formula for the volume of a sphere?
2. How does the surface area formula for a sphere relate to its volume?
3. What is the impact of doubling the radius on the sphere's volume and surface area?
4. Can you apply these formulas to find the properties of a hemisphere?
5. What are the real-life applications of calculating the volume and surface area of a sphere?

**Tip:** Always ensure to substitute the radius accurately in the formulas for volume and surface area to avoid errors in calculations.

Explore how to calculate the volume and surface area of a sphere with a radius of 4 cm. Detailed formulas and step-by-step calculations provided. Suitable for students in Grades 10-12.

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