Question : If the radius of a cylinder is decreased by 50% and the height is increased by 50%, then the volume change is:
Option 1: 52.5%
Option 2: 67.5%
Option 3: 57.5%
Option 4: 62.5%
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Correct Answer: 62.5%
Solution : The volume of a cylinder $V = \pi r^2 h$ where $r$ is the radius and $h$ is the height. The radius of the cylinder is decreased by 50%, the new radius is, $r' = r - 0.50r = 0.50r$ The height of the cylinder is increased by 50%, the new height is, $h' = h + 0.50h = 1.50h$ The volume of the new cylinder, $V' = \pi (r')^2 h' = \pi (0.50r)^2 (1.50h) = 0.375 \pi r^2 h$. The volume change $=\frac{V - V'}{V} ×100= \frac{\pi r^2 h - 0.375 \pi r^2 h}{\pi r^2 h}×100 = 62.5$% Hence, the correct answer is 62.5%.
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Question : If the curved surface area of a cylinder is increased by 20% and height is decreased by 4%, then the net decrease or increase in the volume will be:
Option 1: 36% decrease
Option 2: 20% increase
Option 3: 50% increase
Option 4: 33% decrease
Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6\tfrac{1}{4}$%
Option 3: increased by $6\tfrac{1}{4}$%
Option 4: increased by $6$%
Question : If water is frozen to become ice, its volume is increased by 10%, then if the ice is melted to water again, its volume will be decreased by:
Option 1: $9$%
Option 2: $9\frac{1}{11}$%
Option 3: $8$%
Option 4: $9\frac{1}{2}$%
Question : If the price of a product is first increased by 15% and then decreased by 20%, then what is the percentage change in the price?
Option 1: 5% decrease
Option 2: 8% increase
Option 3: 5% increase
Option 4: 8% decrease
Question : A number is first decreased by 20%. The decreased number is then increased by 20%. The resulting number is less than the original number by 20. Then the original number is:
Option 1: 200
Option 2: 400
Option 3: 500
Option 4: 600
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