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
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Correct Answer: 50% increase
Solution : Given: The curved surface area of a cylinder is increased by 20% and height is decreased by 4%. Let the increase in radius be $x$%. Applying the successive percentage change formula we get, $x-4-\frac{4x}{100}=20$ $⇒\frac{96x}{100}=24$ $⇒x=25$% Let the old radius be $4r$ units and the new radius be $5r$ units. (For 25% increase) Also, let the old height be $25h$ units and the new height be $24h$ units. (For 4% decrease) So, the volume of the old cylinder = $\pi(4r)^2(25h)$ = $400\pi r^2h$ cubic units And the volume of the new cylinder = $\pi(5r)^2(24h)$ = $600\pi r^2h$ cubic units Therefore, the percentage increase in volume = $\frac{600\pi r^2h-400\pi r^2h}{400\pi r^2h}×100=50$% Hence, the correct answer is a 50% increase.
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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%
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 : 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 : The radius of the base and curved surface area of a right cylinder are $r$ units and $4\pi rh$ square units respectively. The height of the cylinder is:
Option 1: $\frac{h}{2}$ units
Option 2: $h$ units
Option 3: $2h$ units
Option 4: $4h$ units
Question : If each side of a cube is decreased by 12%, then the percentage decrease in its surface area is:
Option 1: 25.66%
Option 2: 28.23%
Option 3: 22.56%
Option 4: 26.54%
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