Question : If the radius of a cylinder is decreased by 16 percent, then by how much percent its height must be increased so that the volume of the cylinder remains the same.
Option 1: 32.96 percent
Option 2: 41.72 percent
Option 3: 45.28 percent
Option 4: 36.43 percent
Correct Answer: 41.72 percent
Solution :
Let the initial radius be r and height be 100 and the final height be h
⇒ Final radius = r$({1 - \frac{16}{100})}$ = 0.84r
Initial volume = Final volume
⇒ $\pi r^{2}$ × 100 = $\pi (0.84r)^{2}$h
⇒ h = $\frac{100}{0.7056}$ = 141.72
Increase in height
= 141.72 – 100 = 41.72
⇒ Percentage increase in height = 41.72%
Hence, the correct answer is 41.72%.
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