Question 78

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?

Solution

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)

Share on Whatsapp Share on Whatsapp

Create a FREE account and get: