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
We 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!
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