Question

To find the diameter of a hollow rubber ball, we first need to determine its surface area. Given that each ball costs the company $1 and the cost per square foot is $0.02, we can find the surface area by dividing the total cost by the cost per square foot:

Surface Area = Total Cost / Cost per Square Foot
Surface Area = $1 / $0.02 = 50 square feet

Now, we know that the surface area of a sphere (or ball) is given by the formula A = 4πr^2, where A is the surface area and r is the radius. We can solve for the radius and then find the diameter (which is twice the radius):

Answer 1

To find the diameter of the hollow rubber ball, we need to determine its radius first.

We know that the surface area of the ball is 50 square feet. Using the formula for the surface area of a sphere, which is A = 4πr^2, we can substitute the given surface area and solve for the radius:

50 = 4πr^2

Dividing both sides of the equation by 4π, we get:

r^2 = 50 / (4π)

r^2 ≈ 3.98

Taking the square root of both sides, we find:

r ≈ √3.98

Now that we have the radius, we can calculate the diameter by multiplying the radius by 2:

diameter ≈ 2 * √3.98

Therefore, the approximate diameter of the hollow rubber ball is approximately 3.16 feet.