Question

A rectangular sheet of paperof lengt a and breadth b can be converted into cylinder in two ways if ratio pf volimes is 2:3 find a and b

Answer 1

if converted from breadth-
height of cylinder=b
circumference of base of cylinder=a
2pie r=a
radius of cylinder=a/2pie
Volume of cylinder=(a^2×b)/4pie

if converted from length-
height of cylinder=a
circumference of base of cylinder=b
2pie r=b
radius of cylinder=b/2pie
Volume of cylinder=(b^2×a)/4pie

ratio of volumes=2:3
[(b^2×a)/4pie]÷[(a^2×b)/4pie]=2:3
b/a=2:3
thus b=2x
and a=3x