A toy factor paints all of its rubber balls with 2 coats of of latex for durability. How many square centimeters of latex are needed to cover a rubber ball with a circumference of 16π cm?

1 coat: 256π cm² ≈ 804.25 cm² 2 coats: 512π cm² ≈ 1608.50 cm² (rounds to 1608 cm²)

Step-by-step explanation:

The radius of the ball is ...

r = C / (2π) = (16π cm) / (2π) = 8 cm

The formula for the area of a sphere is ...

A = 4πr²

Filling in the value of the radius, we find the area of the ball to be ...

A = 4π (8 cm) ² = 256π cm² ≈ 804.25 cm²

Then 256π or 804.25 is the number of square centimeters needed to cover the given ball with one coat of latex.

If the ball is only considered to be covered when it has two coats of latex, then twice that amount, 512π or 1608.50 square centimeters of latex are required.