Answer:
4.667 inches
Step-by-step explanation:
The volume of the border is the product of its area and depth. Its area is the product of its width and the length of its centerline.
If x is the width of the border in feet, the diameter of its centerline is ...
d = 88+x
Then the circumference of that circle, the length of the centerline, is ...
C = πd = π(88+x)
and the area is the product of this length and the width of the border:
A = xC = πx(88+x)
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The depth is expected to be 3 inches, or 1/4 foot, and the volume is (3 ft)³ = 27 ft³. So, we have the volume equation ...
V = (1/4)A = 27
πx(88+x)/4 = 27
x^2 +88x = 108/π . . . . . multiply by 4/π
x^2 +88x + 44^2 = 108/π +44^2 . . . . complete the square
(x +44)^2 = (108/π) +1936 . . . . . . . . . .write the equation as a square
We want the solution that is near zero, so, taking the positive square root, we get ...
x = -44 +√(108/π +1936) ≈ 0.388934 . . . . feet
The width in inches is 12 times this value, or about 4.667 inches.
