A tennis ball has a radius of 3.5 cm. A manufacturer wants to provide sufficient
material to cover 100 tennis balls. What area of material is required? Give your
answer to the nearest cm2
.

To find the area of material required to cover 100 tennis balls, we first need to calculate the surface area of one tennis ball. The formula for the surface area \( A \) of a sphere is given by:

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

where \( r \) is the radius. Given that the radius \( r = 3.5 \) cm:

\[
A = 4\pi (3.5)^2
\]

Calculating this step-by-step:

1. Calculate \( (3.5)^2 \):
   \[
   (3.5)^2 = 12.25 \, \text{cm}^2
   \]

2. Calculate \( 4\pi (12.25) \):
   \[
   A = 4 \times 3.14159 \times 12.25 \approx 153.94 \, \text{cm}^2
   \]

Now, to find the total area for 100 tennis balls:

\[
\text{Total Area} = 100 \times 153.94 \approx 15394 \, \text{cm}^2
\]

Rounding this to the nearest cm²:

\[
\text{Total Area} \approx 15394 \, \text{cm}^2
\]

Thus, the area of material required to cover 100 tennis balls is **15,394 cm²**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would the area change if the radius of the tennis balls were increased to 4 cm?
2. What is the volume of a single tennis ball?
3. How much material would be needed for 50 tennis balls?
4. How does the surface area of a sphere compare to that of a cylinder with the same radius and height?
5. If the manufacturer used a different material with a different thickness, how would that affect the total area? 

**Tip:** When calculating areas and volumes of spheres, remember to keep track of the units and convert them as necessary for consistent results.

A tennis ball has a radius of 3.5 cm. A manufacturer wants to provide sufficient material to cover 100 tennis balls. What area of material is required? Give your answer to the nearest cm².

Discover how to calculate the area of material required to cover 100 tennis balls with a radius of 3.5 cm. The solution demonstrates the use of the surface area formula for spheres, resulting in a total area of 15,394 cm².

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