Question

a womens basketball has a radius of 4.5 inches. which answer is closest to the total surface area of the ball (sphere)?

• 13 \\(\text{in}^2\\)
• 254 \\(\text{in}^2\\)
• 1145 \\(\text{in}^2\\)
• 382 \\(\text{in}^2\\)

Explanation:

⚡ Using what you learned: surface area of prisms, pyramids, cylinders, cones, spheres

Step 1: Identify the given values and formula

The object is a sphere (basketball) with a radius:

$$ r = 4.5\text{ in} $$

The formula for the surface area of a sphere is:

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

Step 2: Calculate the surface area

Substitute \( r = 4.5 \) into the formula:

$$ A = 4\pi (4.5)^2 $$

$$ A = 4\pi (20.25) $$

$$ A = 81\pi $$

$$ A \approx 81 \times 3.14159 \approx 254.47\text{ in}^2 $$

Answer:

\( 254\text{ in}^2 \)