Understanding Sphere Surface Area Calculation

The question asks for the surface area of a sphere given its radius and the value of π.

Given Information:

• Radius of the sphere, $r = 14$ cm
• Value of π, $ \pi = \frac{22}{7} $

Formula Needed:

The formula for the surface area (A) of a sphere is:

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

Step-by-Step Calculation

1. Substitute the given values into the formula:

   $$A = 4 \times \frac{22}{7} \times (14 \text{ cm})^2$$

2. Expand the radius squared term:

   $$A = 4 \times \frac{22}{7} \times (14 \text{ cm} \times 14 \text{ cm})$$

3. Simplify the expression by canceling out the common factor of 7:

   $$A = 4 \times 22 \times \left(\frac{14}{7}\right) \times 14 \text{ cm}^2$$

   $$A = 4 \times 22 \times 2 \times 14 \text{ cm}^2$$

4. Perform the multiplication:

   First, multiply 4 by 22:

   $$4 \times 22 = 88$$

   Then, multiply the result by 2:

   $$88 \times 2 = 176$$

   Finally, multiply this by 14:

   $$176 \times 14$$

   To calculate $176 \times 14$:

   $$176 \times 10 = 1760$$

   $$176 \times 4 = 704$$

   $$1760 + 704 = 2464$$

   Therefore, the surface area is:

   $$A = 2464 \text{ cm}^2$$

Result Verification

The calculated surface area is 2464 cm². This matches option 4.