Homework Help: maths-urgently needed

Posted by Anonymous on Wednesday, January 16, 2013 at 12:24pm.

The volume of a cylinder is 48.125 cm3, which is formed by rolling a rectangular paper sheet along the length of the paper. If cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting out the square of side 0.5 cm from each of the four corners of the paper sheet, then what is the volume of this box

maths-urgently needed - Reiny, Wednesday, January 16, 2013 at 4:43pm
let the width of the sheet of paper be x
let its length be y

so the cylinder made from it would have a height of y
the width would be its circumference
2πr = x
r = x/(2π)

volume = πr^2 h = π(x^2/(4π^2) y = x^2 y/(4π)
48.125 = x^2 y/(4π)
192.5π = x^2y
y = 192.5/x^2

now to the box:
length = (y-1)
width = (x-1)
height = .5
volume = .5(x-1)(y-1) = .5(x-1)(192.5/x^2 - 1)
= (1/2)(192.5/x - x - 192.5/x^2 + 1)

getting nowhere .....

not enough information

in the first part, there is no unique solution for x and y
which would change the shape of the sheet of paper, which would change the volume of the resulting box

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