This is the question I have been confused with. Please help me solve it!
A sphere has to be fully wrapped completely in a circular sheet of least area. Find the minimum percentage of the wastage in circular sheet in wrapping it.
My solution is:
Surface area of a sphere= 4 pi R sq.
Imagine the sphere is placed in the middle of a circular sheet in such a way that when you pick the sides of the circular sheet, the two opposite edges just touch each other at the top of the sphere. This means that the radius of such sheet should be the half circumference of of sphere which is pi r
So the radius of the circular sheet is pi r. Hence the area is pi (r sq.) bracket raise to power 2.
Hence the wasted part of the sheet is area of the circular sheet - area of the sphere, which is pi cube r square - 4 pi r square.
Hence the wasted part to total area of the sheet comes out to be 59.43%. But the problem is the in the book the answer is supposed to be 66.6%. There is no explanation.
A sphere has to be fully wrapped completely in a circular sheet of least area. Find the minimum percentage of the wastage in circular sheet in wrapping it.
My solution is:
Surface area of a sphere= 4 pi R sq.
Imagine the sphere is placed in the middle of a circular sheet in such a way that when you pick the sides of the circular sheet, the two opposite edges just touch each other at the top of the sphere. This means that the radius of such sheet should be the half circumference of of sphere which is pi r
So the radius of the circular sheet is pi r. Hence the area is pi (r sq.) bracket raise to power 2.
Hence the wasted part of the sheet is area of the circular sheet - area of the sphere, which is pi cube r square - 4 pi r square.
Hence the wasted part to total area of the sheet comes out to be 59.43%. But the problem is the in the book the answer is supposed to be 66.6%. There is no explanation.
