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October 30, 2014

October 30, 2014

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

- maths-urgently needed -
**Reiny**, Wednesday, January 16, 2013 at 4:43pmlet 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

- maths-urgently needed -
**Jay Bankoti**, Sunday, November 24, 2013 at 11:01amWe do have a way for this question.Only way is to think out of the box. Let me tell you how it goes:

Volume of cylinder= (pi) (r)(r)(h)= 48.125

(r)(r)h = 15.3125

15.3125 is not a perfect square. To make it perfect square, h should be 5cm.

Now (r)(r)=15.3125/5 = 3.0625 which makes r = 1.75cm

Therefore, rectangular sheet has length of 2(pi)(r)=11cm and width (h) of 5cm.

After cutting a square of 0.5cm from each corner, the dimension of the cuboid becomes:

Length=11-1=10cm; Breadth=5-1=4cm; Height=0.5cm.

Therefore, Volume of cuboid= 10 x 4 x 0.5 = 20 cubic cm.

Thank you for reading it!

Have a nice day Reiny!

Jay Bankoti

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