UPSC CDS 1 2022 Math Paper

Given:
Length of rectangular sheet =x ,
Breadth of rectangular sheet =y
Volume of the cylinder formed by rolling the sheet along with its breadth =p
Volume of the cylinder formed by rolling the sheet along with its length =q
Formula Used:
Volume of Cylinder =πr2h
Circumference =2πr
Where r and h are the radius and height of the cylinder respectively.
Calculation:
Let, x and y are length and breadth of cylinder
According to the question, q=2p
⇒π‌

x2

4π2

y=2π‌

y2

4π2

x
⇒x2y=2y2x
∴x=2y