Solution:
Solution:
How to find the diameter of the ball?
Remember that for a sphere of diameter D, the surface area is:
[tex]\begin{gathered} A=4\pi(\frac{D}{2})^2 \\ r=\frac{D}{2} \end{gathered}[/tex]In this case, the cost is $0.02 per square foot, and the company wants to expend (at maximum) $1 per ball, so first we need to solve:
[tex]\begin{gathered} 0.02\times A=1 \\ A=\frac{1}{0.02} \\ A=50 \end{gathered}[/tex]By substituting the values of A=50 in the formula below, we will have
[tex]\begin{gathered} \begin{equation*} A=4\pi(\frac{D}{2})^2 \end{equation*} \\ 50=4\times\frac{22}{7}\times(\frac{D^2}{4}) \\ 50=\frac{22D^2}{7} \\ cross\text{ multiply} \\ 50\times7=22D^2 \\ 22D^2=350 \\ \frac{22D^2}{22}=\frac{350}{22} \\ D^2=\frac{350}{22} \\ D=\sqrt{\frac{350}{22}} \\ D=4.0feet \end{gathered}[/tex]Hence,
Since the company wants to spend a maximum $1,
The diameter of the new rubber ball, to the nearest foot, must be D = 4.0 ft (in the case of the maximum cost).
Hence,
