The diameter of a new ball is 4.0ft
According to the statement
we have given that the the company wants to spend a maximum of $1 each.
And we have to find a diameter of a new ball.
Remember that for a sphere of diameter D, the surface area is
A = 4*pi*(D/2)^2
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:
$0.02*A = $1
A = $1/$0.02 = 50
So the surface of the ball must be 50 square feet.
Then we solve:
50ft^2 = 4*3.14*(D/2)^2
D = 2*√(50 ft^2/(4*3.14)) = 4.0 ft
here the diameter of a ball is 4.0ft.
So, The diameter of a new ball is 4.0ft
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