Question

billiards company is designing limited-edition billiard balls covered in 24-carat gold foil. The company needs to calculate how much gold foil is needed to cover the entire surface of the ball. If the diameter of the ball is 2.25 inches, what's the surface area of the ball? Round to the nearest tenth of a square inch. A. 15.9 in2 B. 17.5 in2 C. 12.4 in2 D. 19.2 in2

Answer 1

Answer: The surface area of the ball is 15.90 in².

Step-by-step explanation:

1. The ball is spherical, therefore to calculate its surface area, you must apply the formula for calculate the surface area of a sphere, which is:

$SA=4r^{2}\pi$

2. You can calculate the radius ($r$) with the diameter given in the problem, as following:

$r=\frac{2.25in}{2}\\r=1.125in$

3. Substitute this value into the formula. Then, you obtain that the result is:

$SA=4(1.125)^{2}\pi\\SA=15.90in^{2}$