Three rectangles A₁, A₂ and A₃ have the same area. Their lengths a₁, a₂ and a₃ respectively are such that… · ABC26GN4890
Subject: General Aptitude · Chapter: Volume and Surface Area
Three rectangles $A_{1}, A_{2}$ and $A_{3}$ have the same area. Their lengths $a_{1}, a_{2}$ and $a_{3}$ respectively are such that $a_{1}<a_{2}<a_{3}$. Cylinders $C_{1}, C_{2}$ and $C_{3}$ are formed from $A_{1}, A_{2}$ and $A_{3}$ respectively by joining the parallel sides along the breadth. Then
(a)$C_{1}$ will enclosed maximum volume
(b)$C_{2}$ will enclosed maximum volume
(c)$C_{3}$ will enclosed maximum volume
(d)Each of $C_{1}, C_{2}$ and $C_{3}$ will enclose equal volume
Answer
Answer (as printed): C
Explanation
Let the breadths of the rectangles $A_{1}, A_{2}$ and $A_{3}$ be $b_{1}, b_{2}$ and $b_{3}$ respectively. Since the rectangles have the same area and $a_{1}<a_{2}<a_{3}$, we have: $b_{1}>b_{2}>b_{3}$. When the rectangles are folded to form cylinders, then their lengths $a_{1}, a_{2}, a_{3}$ determine the radii of the cylinders while their breadths $b_{1}, b_{2}, b_{3}$ form their heights. Volume of cylinder $=\pi r^{2} h$. Clearly, the rectangle $A_{3}$ with length $a_{3}$ shall have maximum value of $r^{2}$ and hence $C_{3}$ has maximum volume.
Explanation as extracted from the printed page; notation may be imperfect.