SOLUTION: A two-dimesional, silo-shaped figure is formed by placing a semicircle of diameter 1 on top of a unit square, with the diameter coinciding with the top of the square. What is the r

Question 325280: A two-dimesional, silo-shaped figure is formed by placing a semicircle of diameter 1 on top of a unit square, with the diameter coinciding with the top of the square. What is the radius of the smallest circle that contains this figure?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Draw the semi-circle about the origin, x^2 + y^2 = 0.25
The top point is (0,0.5)
Draw the square under it. The corners are (-0.5,-1) and (0.5,-1)
The 3 points make an isoceles triangle. The base is 1.
The 2 equal sides are sqrt(0.5^2 + 1.5^2)
= sqrt(2.5) = sqrt(10)/2
-------------------------
R = a^2b/4K K = area
K = bh/2 = 1*1.5/2 = 3/4
R = (10/4)*1/3 = 5/6 units
-------------------------
The circle is (x)^2 + (y+1/3)^2 = (5/6)^2

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