Homework Help: math

Posted by rajshekhar on Monday, February 1, 2010 at 6:05am.

A rectangular sheet of metal, of area 440 sq.cm is folded into a cylinder, to enclose a volume of 1540 cu.cm. A circle whose diameter is equal to the width of the rectangular sheet is cut from the sheet. Find the ratio of the area of the uncut region to the area of the cut region?

math - Reiny, Monday, February 1, 2010 at 10:25am
let the radius of the cylinder formed be x cm
then the length of the rectangle is 2pi(x)
let the width of the rectangle by y cm

pi(x^2)(y) = 1540
2pi(x)(y) = 440
divide first by second
x/2 = 3/5
x = 7

so area cut out = pi(7)^2 = 49pi
uncut area = 440 - 49pi

ratio of uncut:cut
= (440-49pi)/(49pi)

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