If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?
Let radius of cylinder = 10 cm and height = 10 cm
=> Volume = $$\pi r^2h$$
= $$\pi (10)^2\times10=1000\pi$$
If radius is decreased by 20%, => new radius = $$\frac{80}{100}\times10=8$$ cm
=> $$\pi r^2h=1000\pi$$
=> $$(8)^2h=1000$$
=> $$h=\frac{1000}{64}=\frac{125}{8}=15.625$$
$$\therefore$$ Increase in height = $$\frac{(15.625-10)}{10}\times100$$
= $$5.625\times10=56.25\%$$
=> Ans - (C)
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