Question : If the radius of a cylinder is increased by 25%, by how much percentage the height must be reduced, so that the volume of the cylinder remains the same.
Option 1: 36
Option 2: 56
Option 3: 64
Option 4: 46
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Correct Answer: 36
Solution : Given: The radius of a cylinder is increased by 25%. Volume of the cylinder = $\pi r^2 h$ Let $h$ be the initial height, $r$ be the initial radius, $H$ be the final height and the new radius will be $\frac{125}{100}r$ = $\frac{5}{4}r$. According to the question, $\pi\times r^2\times h=\pi\times(\frac{5}{4}r)^2\times H$ $⇒h=\frac{25}{16}\times H$ $⇒\frac{h}{H}=\frac{25}{16}$ The decrease in percentage in the height is $\frac{(h-H)}{h}\times 100$ = $\frac{(25-16)}{25}\times 100$ = 9 × 4 = 36% Hence, the correct answer is 36.
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Question : If the radius of a right circular cylinder open at both ends is decreased by 25% and the height of the cylinder is increased by 25%, the curved surface area of the cylinder thus formed:
Option 1: remains unaltered
Option 2: is increased by $25\%$
Option 3: is increased by $6.25\%$
Option 4: is decreased by $6.25\%$
Question : If the radius of a cylinder is decreased by 20% and the height is increased by 20% to form a new cylinder, then the volume will be decreased by:
Option 1: 23.2%
Option 2: 22.3%
Option 3: 32.2%
Option 4: 20.5%
Question : The radius of a cylinder is 10 cm and the height is 4 cm. The number of centimeters that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is:
Option 1: 5 cm
Option 2: 4 cm
Option 3: 25 cm
Option 4: 16 cm
Question : The length and breadth of a cuboid are increased by 20% and 25%, respectively, while its height is reduced by 30%. What must be the total percentage increase/decrease in the volume of the cuboid?
Option 1: Increase by 5%
Option 2: Increase by 3%
Option 3: Decrease by 2%
Option 4: Decrease by 4%
Question : A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percentage of the material is wasted in this process?
Option 1: 25
Option 2: 0
Option 3: 5
Option 4: 10
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