UPSC CDS Math Volume and Surface Area Questions

Let y1,y2 and y3 be the breadths of the rectangles R1,R2 and R3 , respectively.Suppose the area of the rectangles be A.
∴x1×y1=A⇒y1=‌‌

A

x1

x2×y2=A⇒y2=‌‌

A

x2

x3×y3=A⇒y3=‌‌

A

x3

Let r1,r2 and r3 be the radius of the cylinders formed from the rectangles by joining the parallel sides along the breadth.
∴r1=

x1

2π

,r2=

x2

2π

and r3=

x3

2π

Now,
=‌‌

A

4π

×x1
=‌‌

A

4π

×x2
=‌‌

A

4π

×x3
Given, x1<x2<x3
⇒

A

4π

×x1<

A

4π

×x2<

A

4π

×x3
⇒V1<V2<V3