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The problem involves calculating the **surface area** and **volume** of a spherical beach ball, given its diameter. Let's break down the solution step by step.

### **Given:**
- Diameter of the beach ball = 40 cm  
- Therefore, **radius** \( r = \frac{40}{2} = 20 \, \text{cm} \)  
- Use \( \pi = 3.1416 \)

---

### **(a) Surface Area of the Sphere:**
The formula for the surface area of a sphere is:

\[
A = 4 \pi r^2
\]

Substitute \( r = 20 \, \text{cm} \) and \( \pi = 3.1416 \):

\[
A = 4 \times 3.1416 \times (20)^2
\]

\[
A = 4 \times 3.1416 \times 400 = 5026.56 \, \text{cm}^2
\]

---

### **(b) Volume of the Sphere:**
The formula for the volume of a sphere is:

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

Substitute \( r = 20 \, \text{cm} \) and \( \pi = 3.1416 \):

\[
V = \frac{4}{3} \times 3.1416 \times (20)^3
\]

\[
V = \frac{4}{3} \times 3.1416 \times 8000
\]

\[
V = \frac{4}{3} \times 25132.8 = 33509.07 \, \text{cm}^3
\]

---

### **Final Answers:**
- **Surface Area:** \( 5026.56 \, \text{cm}^2 \)  
- **Volume:** \( 33509.07 \, \text{cm}^3 \)

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Do you have any further questions or need additional clarifications?

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### **Related Questions:**
1. What is the surface area of a sphere with a radius of 10 cm?
2. How does the volume of a sphere change if its radius is doubled?
3. What is the ratio of the surface area to volume for a sphere?
4. If the diameter of a sphere is halved, how much smaller is the volume?
5. How can you apply these formulas to other 3D shapes?

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**Tip:** Always ensure correct units are used in surface area (square units) and volume (cubic units) calculations!

The diagram shows a beach ball. a) Find the surface area of the beach ball. b) Find the volume of the beach ball.

Calculate the surface area and volume of a spherical beach ball with a 40 cm diameter. Learn how to apply the formulas for the surface area and volume of a sphere, step by step. Suitable for high school students.

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