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%
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Correct Answer: 56.76%
Solution : Given: the cylinder's base radius = 21 cm and height = 16 cm Let the base radius and height of the original cylinder be $r$ and $h$ respectively. ⇒ The base radius and height of the smaller cylinder are $r$ and $\frac{h}{2}$ respectively. Now, the surface area of the original cylinder = $2\pi r(r+h)$ and the surface area of the smaller cylinders = $2×2\pi r(r+\frac{h}{2})$ = $2\pi r(2r+h)$ So, the increase in area = $2\pi r(2r+h)-2\pi r(r+h)$ = $2\pi r^2$ Thus, increase percentage = $\frac{\text{increased area}}{\text{original area}}×100$ = $\frac{2\pi r^2}{2\pi r(r+h)}×100$ = $\frac{r}{r+h}×100$ = $\frac{21}{21+16}×100$ = $\frac{21}{37}×100$ $\approx$ 56.76% Hence, the correct answer is 56.76%.
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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%
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 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
Question : If the curved surface area of a cylinder is 440 cm2 and the height of the cylinder is 10 cm, then what is the radius (in cm.) of the cylinder?
Option 1: 7
Option 2: 14
Option 3: 21
Option 4: 3.5
Question : The radius of a right circular cylinder is 7 cm. Its height is thrice its radius. What is the curved surface area of the cylinder?
Option 1: 724 cm2
Option 2: 666 cm2
Option 3: 924 cm2
Option 4: 264 cm2
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