Question

3. A person has a rectangular sheet of
metal. He has to make cylinderical
vessel whose both circular ends
are closed. When he minimize the
wastage of the sheet, then what is
the ratio of the wasted sheet to the
utilised sheet? (π=22/7)

Answer 1

Answer:

1/11

Step-by-step explanation:

Wastage will be minimum when rectangular sheet is cut in the fashion as shown in attached image.

l - 2b is the circumference of the circle.

so, 2.π. r  = l - 2b

π. b = i - 2b

∴ l = π.b + 2 b

Utilized Area = Area of rectangle  + Area of Circle 1 + Area of Circle 2

∴ Utilized Area =  (l - 2b) b + π.b²/4 + π.b²/4 = 3π.b²/2

Wasted Area = Area of rectangular sheet - Utilized Area

∴ Wasted Area = lb - 3π.b²/2 =  (π.b + 2 b)b - 3π.b²/2 = (2 - π/2).b²

So, the ratio of Wasted Area/Utilized Area = (2 - π/2).b²/3π.b²/2

∴  ratio of Wasted Area/Utilized Area = 1/11