Question : If the height of the cylinder is increased by 35% and the radius is increased by 10%, what will be the percentage increase in the curved surface area of a cylinder?
Option 1: 46.5
Option 2: 45
Option 3: 48.5
Option 4: 49.7
Correct Answer: 48.5
Solution :
Let, original height = $h$
Original radius = $r$
So, the Curved surface area of the cylinder = $2\pi r h $
After 35% increase, height = $h+h\times \frac{35}{100}=1.35h$
After 10% increase, radius = $r+r\times\frac{10}{100}=1.1r$
So, the new curved surface area of the cylinder = $2\pi \times1.1r\times 1.35h=2.97\pi rh$
Hence, percentage increase = $\frac{2.97\pi rh-2\pi rh}{2\pi rh}\times100=48.5\%$
Hence, the correct answer is 48.5.
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