Question : A solid cylinder having a radius of base of 28 cm and a height of 24 cm is bisected from its height to get two identical cylinders. What will be the percentage increase in the total surface area?
Option 1: 61.72%
Option 2: 41.92%
Option 3: 53.85%
Option 4: 48.64%
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Correct Answer: 53.85%
Solution : Given, Radius = 28 cm and Height = 24 cm Let the radius and height of the cylinder be $r$ and $h$ respectively. ⇒ Radius and height of smaller cylinder are $r$ and $\frac{h}{2}$ The surface area of the old cylinder = $2πr^2 + 2πrh = 2πr(r + h)$ And The combined surface area of 2 small cylinder $= 2(2πr(r + \frac{h}{2})) ⇒ 2πr(2r + h)$ ⇒ Increase in area $= 2πr(2r + h) – 2πr(r + h) = 2πr(r) = 2πr2$ So, the required percentage increase = $100 × \frac{2\pi r^2}{2πr(r + h)}$ = $100 × \frac{r}{r+h}$ = $100 × \frac{28}{28+24}$ = $100 × \frac{28}{52}$ = $53.85$% Hence, the correct answer is 53.85%.
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Question : A solid cylinder having a radius of base of 21 cm and a height of 16 cm is bisected from its height to get two identical cylinders. What will be the percentage increase in the total surface area?
Option 1: 56.76%
Option 2: 42.52%
Option 3: 62.34%
Option 4: 48.88%
Question : A sphere of radius 18 cm is melted and then a solid cylinder of base radius 4 cm is made from it. What is the height of the solid cylinder?
Option 1: 196 cm
Option 2: 486 cm
Option 3: 224 cm
Option 4: 384 cm
Question : The curved surface area of a cylinder is 968 cm2. If the height of the cylinder is 11 cm, then what will be the diameter of its base?
Option 1: 26 cm
Option 2: 22 cm
Option 3: 28 cm
Option 4: 24 cm
Question : The circumference of the base of a cylinder is $28 \pi$ cm. If the height of the cylinder is 17 cm, then what will be the curved surface area of the cylinder?
Option 1: $372 \pi ~\text{cm}^2$
Option 2: $436\pi \ \text{cm}^2$
Option 3: $524\pi \ \text{cm}^2$
Option 4: $476\pi \ \text{cm}^2$
Question : The radius of a cylinder is 14 cm. If the height of the cylinder is four times of its radius, then what is the curved surface area of the cylinder?
Option 1: 5546 cm2
Option 2: 4928 cm2
Option 3: 4694 cm2
Option 4: 5214 cm2
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