Question : The radius of a sphere is doubled. The percentage increase in its surface area is ______.
Option 1: 75%
Option 2: 100%
Option 3: 300%
Option 4: 400%
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Correct Answer: 300%
Solution : Let the radius of the sphere be $r$ units. So, the surface area of the sphere = $4\pi r^2$ sq. units After doubling, the new radius = 2$r$ units So, the new surface area = $4\pi (2r)^2=16\pi r^2$ sq. units $\therefore$ The percentage increase = $\frac{16\pi r^2-4\pi r^2}{4\pi r^2}×100=\frac{12\pi r^2}{4\pi r^2}×100= 300\%$ Hence, the correct answer is 300%.
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Question : The surface area of a sphere is 2464 cm². Find the radius of the sphere. [Use $\pi=\frac{22}{7}$ ]
Option 1: 14 cm
Option 2: 28 cm
Option 3: 42 cm
Option 4: 40 cm
Question : If the curved surface area of a solid cylinder is two-fifths of its total surface area, then what is the ratio of its diameter to its height?
Option 1: 2 : 5
Option 2: 1 : 2
Option 3: 2 : 3
Option 4: 3 : 1
Question : The radius of a circle is increased by 10%. The percentage increase in its area is:
Option 1: 10%
Option 2: 11%
Option 3: 20%
Option 4: 21%
Question : If each edge of a cube is increased by 40%, the percentage increase in its surface area is:
Option 1: 40%
Option 2: 60%
Option 3: 80%
Option 4: 96%
Question : The radius of a sphere is 14 cm. What is the surface area of this sphere? [Use $\pi=\frac{22}{7}$]
Option 1: 2464 cm2
Option 2: 1232 cm2
Option 3: 1848 cm2
Option 4: 616 cm2
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