Question

Find the ratio of the volumes of the two cylinders formed by rolling an iron sheet 2.2m x 1.m ether along its length or by rolling along its breadth.

Answer 1

Dimensions of iron sheet = 2.2m x 1.5m
Let the iron sheet be rolled along its length to form a cylinder, thus the length and breadth of the sheet will be equal to circumference and height (h) of the cylinder respectively.
Let r be the radius of the cylinder
Circumference cylinder = 2.2m
2 x π x r = 2.2

r = `(2.2)/(2π)`

r = `(1.1)/π"m"`
Thus,
Volume of the cylinder so formed
= π x r² x h

= `π xx (131/π)^2 xx 1.5`

= `(1.815)/π"m"^3` .................................(1)
Now,
Let the iron sheet be rolled along its breadth to form a cylinder, thus the length and breadth of the sheet will be equal to height (H) and circumference of the cylinder respectively.
Let R be the radius of the cylinder.
Circumference of cylinder = 1.5m
2 x π x R = 1.5

R = `(1.5)/(2π)`

R = `(0.75)/π"m"`
thus,
Volume of the cylinder so formed
= π x R² x H

= `π xx (0.75/π)^2 xx 2.2`

= `(1.2375)/π"m"^2`   ..........................(2)

∴ Ratio of volumes of two cylinders

= `((1))/((2)`

= `(1.815)/(1.2375) xx (10,000)/(10,000)`

= `(18150)/(12375)`
= 22 : 15.