Calculating Ball Surface Area

The question asks us to find the surface area of a ball (which is a sphere) given its radius. We are also provided with a specific value to use for pi ($\pi$).

Key Information Provided:

• Shape: Ball (Sphere)
• Radius ($r$): 21 mm
• Value of Pi ($\pi$): $\frac{22}{7}$

Surface Area Formula for a Sphere

To calculate the surface area of a sphere, we use the standard mathematical formula:

$$A = 4 \pi r^2$$

Where:

• $A$ represents the surface area.
• $\pi$ is the mathematical constant pi.
• $r$ is the radius of the sphere.

Step-by-Step Calculation

Now, let's substitute the given values into the formula:

1. Substitute values: Plug in $r = 21$ mm and $\pi = \frac{22}{7}$ into the formula.

   $$A = 4 \times \frac{22}{7} \times (21 \text{ mm})^2$$

2. Calculate radius squared: First, find the value of $r^2$.

   $$(21 \text{ mm})^2 = 21 \times 21 \text{ mm}^2 = 441 \text{ mm}^2$$

3. Substitute $r^2$ back into the formula:

   $$A = 4 \times \frac{22}{7} \times 441 \text{ mm}^2$$

4. Simplify the expression: We can simplify the calculation by cancelling out the 7 in the denominator with one of the factors of 441 (since $441 = 7 \times 63$). Alternatively, we can calculate $21/7 = 3$ first. Let's do that:

   $$A = 4 \times \frac{22}{7} \times 21 \times 21 \text{ mm}^2$$

   $$A = 4 \times 22 \times \frac{21}{7} \times 21 \text{ mm}^2$$

   $$A = 4 \times 22 \times 3 \times 21 \text{ mm}^2$$

5. Perform multiplication: Multiply the remaining numbers.

   $$A = 88 \times 63 \text{ mm}^2$$

   Let's calculate $88 \times 63$:
   $88 \times 60 = 5280$
   $88 \times 3 = 264$
   $5280 + 264 = 5544$

   Therefore,

   $$A = 5544 \text{ mm}^2$$

Final Answer Verification

The calculated surface area is $5544 \text{ mm}^2$. Comparing this result with the given options, we find that it matches one of the choices.

Result: The surface area of the ball is $5544 \text{ mm}^2$.