SOLUTION: A square piece of cloth of maximum size is cut from a circular piece, and then a circular piece of maximum size is cut from the sqaure piece. If the radius of the original piece of

Algebra ->  Circles -> SOLUTION: A square piece of cloth of maximum size is cut from a circular piece, and then a circular piece of maximum size is cut from the sqaure piece. If the radius of the original piece of      Log On


   

Question 1147339: A square piece of cloth of maximum size is cut from a circular piece, and then a circular piece of maximum size is cut from the sqaure piece. If the radius of the original piece of cloth was 72 cm, what is the amount of cloth, in cm² that was wasted?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A square piece of cloth of maximum size is cut from a circular piece, and then a circular piece of maximum size is cut from the square piece.
If the radius of the original piece of cloth was 72 cm, what is the amount of cloth, in cm² that was wasted?
:
Find the area of the original piece of Cloth: pi%2A72%5E2 = 16,286 sq/m
:
The diameter, of the original circle is the diagonal of the inscribed square
2 * 72 = 144 cm
the side of this square:
2s^2 = 144^2
s^2 = 144%5E2%2F2
s = sqrt%28144%5E2%2F2%29
s = 101.8 cm is the side of the square
the diameter of the of inscribed circle in the square = to the side of the square
therefore:
r = 101.8/2 = 50.9 cm
area of the this circle: pi%2A50.9%5E2 = 8143 sq/cm
the wasted matierial
16286 - 8143 = 8,143 sq/cm or half is wasted