https://file.aiquickdraw.com/mathbot/file/1728889745033xp94nssy.jpg

The beach ball in the image is a sphere, and the given diameter is 40 cm. We'll use the formulas for the surface area and volume of a sphere to solve the two parts.

### Part a) Surface Area
The formula for the surface area \( A \) of a sphere is:
\[
A = 4\pi r^2
\]
Where:
- \( r \) is the radius of the sphere.
- \( \pi = 3.14 \)

The diameter is given as 40 cm, so the radius is:
\[
r = \frac{40}{2} = 20 \, \text{cm}
\]

Now, calculating the surface area:
\[
A = 4 \times 3.14 \times (20)^2 = 4 \times 3.14 \times 400 = 5024 \, \text{cm}^2
\]

### Part b) Volume
The formula for the volume \( V \) of a sphere is:
\[
V = \frac{4}{3}\pi r^3
\]

Using the radius \( r = 20 \) cm:
\[
V = \frac{4}{3} \times 3.14 \times (20)^3 = \frac{4}{3} \times 3.14 \times 8000 = 33493.33 \, \text{cm}^3
\]

### Final Results:
- **Surface Area**: \( 5024 \, \text{cm}^2 \)
- **Volume**: \( 33493.33 \, \text{cm}^3 \)

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:
1. How would the surface area change if the diameter were doubled?
2. How does the volume of a sphere compare to the volume of a cylinder with the same radius and height?
3. Can you derive the formula for the surface area of a sphere from first principles?
4. What are the units of the surface area and volume if the radius is measured in meters instead of centimeters?
5. How would you calculate the surface area and volume of a hemisphere (half of a sphere)?

**Tip**: Remember, the surface area grows with the square of the radius, but the volume grows with the cube of the radius.

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

Learn how to calculate the surface area and volume of a beach ball with a diameter of 40 cm. Using the formulas for the surface area and volume of a sphere, we'll find the results step by step. Suitable for students in Grades 7-9.

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