Final answer:
The maximum diameter of the new rubber ball the company can manufacture while spending up to $1 each is 4.0 feet, calculated based on the given cost per square foot and the formula for the surface area of a sphere.
Step-by-step explanation:
To find the diameter of the new ball that a company can manufacture while spending a maximum of $1 each, we first need to calculate the maximum area that they can cover with $1, knowing the cost is $0.02 per square foot. Since $1 divided by $0.02 gives us 50 square feet, this is the maximum area for the surface of the ball. The surface area of a sphere can be calculated using the formula A = 4πr², where A is the surface area and r is the radius.
Setting the surface area equal to 50 square feet, the equation becomes 50 = 4πr². To solve for r, divide both sides by 4π to get r² = ≈ 3.9789, and then take the square root to find r. We find that r ≈ 1.9945 feet. Since the diameter is twice the radius, the diameter of the ball is ≈ 3.989 feet. Rounded to the nearest tenth of a foot, the diameter of the new ball is 4.0 feet.