A metal cylinder (solid) of height ‘h' and radius ‘r' is molded into a hollow cylinder of outer radius ‘r' and inner radius ‘r/2'. the percentage increase in the height of hollow cylinder to a solid cylinder of height h is:
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Volume of a cylinder =πr2h=πr2h where rr = radius and hh = height
When diameter of the cylindrical jar is increased by 25%,25%,
new radius = 125r100=5r4125r100=5r4
Let xx be the new height
Volume =π(5r4)2x=25πr2x16=π(5r4)2x=25πr2x16
Since volume remains same, πr2h=25πr2x16πr2h=25πr2x16
⇒x=16h25⇒x=16h25
Decrease in height =(h−x)=(h−16h25)=9h25=(h−x)=(h−16h25)=9h25
Required percentage =(9h25)×100h=36%
When diameter of the cylindrical jar is increased by 25%,25%,
new radius = 125r100=5r4125r100=5r4
Let xx be the new height
Volume =π(5r4)2x=25πr2x16=π(5r4)2x=25πr2x16
Since volume remains same, πr2h=25πr2x16πr2h=25πr2x16
⇒x=16h25⇒x=16h25
Decrease in height =(h−x)=(h−16h25)=9h25=(h−x)=(h−16h25)=9h25
Required percentage =(9h25)×100h=36%
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