Question : If the height of the cylinder is increased by 35% and the radius is increased by 10%, what will be the percentage increase in the curved surface area of a cylinder?
Option 1: 46.5
Option 2: 45
Option 3: 48.5
Option 4: 49.7
Correct Answer: 48.5
Solution : Let, original height = $h$ Original radius = $r$ So, the Curved surface area of the cylinder = $2\pi r h $ After 35% increase, height = $h+h\times \frac{35}{100}=1.35h$ After 10% increase, radius = $r+r\times\frac{10}{100}=1.1r$ So, the new curved surface area of the cylinder = $2\pi \times1.1r\times 1.35h=2.97\pi rh$ Hence, percentage increase = $\frac{2.97\pi rh-2\pi rh}{2\pi rh}\times100=48.5\%$ Hence, the correct answer is 48.5.
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Question : Which of the following statements is not correct?
Option 1: For a given radius and height, a right circular cone has a lesser volume than a right circular cylinder.
Option 2: If the side of a cube is increased by 10%, the volume will increase by 33.1%.
Option 3: If the radius of a sphere is increased by 20%, the surface area will increase by 40%.
Option 4: Cutting a sphere into 2 parts does not change the total volume.
Question : What is the radius of a normal cylinder whose height is 21 cm and curved surface area is 1386 cm2?
Option 1: 10.5 cm
Option 2: 3.5 cm
Option 3: 7 cm
Option 4: 10 cm
Question : What is the curved surface area (in cm2) of a cylinder having a radius of base as 14 cm and height as 10 cm?
Option 1: 440
Option 2: 880
Option 3: 220
Option 4: 1320
Question : If the radius of a circle is increased by 10%, what will be the percentage increase in the area of the circle?
Option 1: 19
Option 2: 20
Option 3: 21
Option 4: 23
Question : The radius of the ends of a frustum of a solid right-circular cone 45 cm high is 28 cm and 7 cm. If this frustum is melted and reconstructed into a solid right circular cylinder whose radius of base and height are in the ratio 3: 5, find the curved surface area (in ${cm}^2$ ) of this cylinder. [Use $\pi=\frac{22}{7}$.]
Option 1: 4580
Option 2: 4610
Option 3: 4640
Option 4: 4620
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