Question

THE VOLUME OF A CYLINDER IS 48.125cm cube , WHICH IS FORMED BY ROLLING A RECTANGULAR PAPER SHEET ALONG THE LENTH OF THE PAPER . IF A CUBOIDAL BOX ( WITHOUT ANY LID i.e , OPEN AT THE TOP ) IS MADE FROM THE SAME SHEET OF PAPER BY CUTTING OUT THE SQURE OF SIDE 0.5 cm FROM EACH OF THE FOUR CORNERS OF PAPER SHEET, THEN WHAT IS THE VOLUME OF THE BOX ?

Answer 1

If the radius of the cylinder is r,

v = πr^2 h, so h = v/(πr^2)
a = 2πrh

now the sheet is w by h, so w = 2πr by v/(πr^2)

the volume of the box is thus

1/2 (w-1)(h-1) = 1/2 (2πr-1)(v/(πr^2) - 1)

since no information was given regarding the relative dimensions of the cylinder, the rectangular sheet could be anything between long and skinny or square.

Answer 2

Steve, don't lose patience.This problem does have answer, only thing is one should 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 bro!
Jay Bankoti

Answer 3

Let length of paper be l and width be b
so (pi)r^2 b=48.125
r^2 = 48.125/ (pi)*b ..(I)
l = 2(pi)r
so r= l/2(pi).....(II)
from I and II
l^2/4(pi)^2 = 48.125/(pi)b
solving we get
l^2 b = 48.125 *4*(pi)
taking value of
pi as 22/7 we get

l^2*b = 55 * 11
l^2*b = 11*11*5
so l=11
b=5

for cuboid
(l-1)*(b-1)*0.5
=10*4*0.5
=20