Question

A rectangular sheet of paper 30 cm x 18 cm can be
transformed into the curved surface of a right circular
cylinder in two ways either by rolling the paper along
its length or by rolling it along its breadth. Find the
ratio of the volumes of the two cylinders thus formed.​

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Dimension = 30cm × 18cm

First situation :-

Paper is rolled along its length :-

So,

2πr1 = 30

r1 = 30/2π

r1 = 15/π cm

Now,

h1 = 18 cm

Then,

Volume of cylinder :-

V1 = π(r1)²h1

Putting value we get :-

V1 = π × (15/π)² × 18

V1 = (225 × 18) /π cm³

Now

Second Situation :-

Paper is rolled along its breadth :-

2πr = 18

r2 = 18/2π

r2 = 9/π cm

h2 = 30 cm

Then,

Volume of cylinder :-

V2 = π(r2)²h2

V2 = π × (9/π)² × 30

V2 = (81 × 30)/π cm³

So,

Ratio = V1 : V2

= (225 × 18)/π : (81 × 30)/π

= (225 × 18)/(81 × 30)

= 5/3

V1 : V2 = 5 : 3