Question : If the curved surface area of a cylinder is increased by 20% and height is decreased by 4%, then the net decrease or increase in the volume will be:
Option 1: 36% decrease
Option 2: 20% increase
Option 3: 50% increase
Option 4: 33% decrease
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Correct Answer: 50% increase
Solution :
Given: The curved surface area of a cylinder is increased by 20% and height is decreased by 4%.
Let the increase in radius be $x$%.
Applying the successive percentage change formula we get,
$x-4-\frac{4x}{100}=20$
$⇒\frac{96x}{100}=24$
$⇒x=25$%
Let the old radius be $4r$ units and the new radius be $5r$ units. (For 25% increase)
Also, let the old height be $25h$ units and the new height be $24h$ units. (For 4% decrease)
So, the volume of the old cylinder = $\pi(4r)^2(25h)$ = $400\pi r^2h$ cubic units
And the volume of the new cylinder = $\pi(5r)^2(24h)$ = $600\pi r^2h$ cubic units
Therefore, the percentage increase in volume = $\frac{600\pi r^2h-400\pi r^2h}{400\pi r^2h}×100=50$%
Hence, the correct answer is a 50% increase.
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