Question : A solid sphere of diameter 7 cm is cut into two equal halves. What will be the increase in its total surface area?
Option 1: 77 cm2
Option 2: 60.5 cm2
Option 3: 65.5 cm2
Option 4: 55 cm2
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Correct Answer: 77 cm2
Solution : Given: Diameter = 7 cm $\therefore r = \frac{7}{2}$ Initial surface area $=4\pi r^2 $ Final surface area $= 4\pi r^2 + 2\pi r^2= 6\pi r^2$ Increase in total surface area $ =6\pi r^2 - 4\pi r^2$ $ = 2\pi r^2$ $= 2×\frac{22}{7}×( \frac{7}{2})^2$ $= 77$ cm2 Hence, the correct answer is 77 cm2.
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Question : The radius of a sphere is 3.5 cm. What is the total surface area of the sphere?
Option 1: 154 cm2
Option 2: 77 cm2
Option 3: 231 cm2
Option 4: 188 cm2
Question : The total surface area of a solid hemisphere of diameter 14 cm is (use $\pi=\frac{22}{7}$ ):
Option 1: 522 cm2
Option 2: 462 cm2
Option 3: 428 cm2
Option 4: 584 cm2
Question : Find the volume of a solid sphere whose diameter is 42 cm. (Use $\pi=\frac{22}{7}$)
Option 1: 38807 cm3
Option 2: 38808 cm3
Option 3: 38806 cm3
Option 4: 38805 cm3
Question : If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2. The radius of the sphere initially was: (use $\pi =\frac{22}{7}$)
Option 1: 4 cm
Option 2: 5 cm
Option 3: 3 cm
Option 4: 6 cm
Question : The difference between the total surface area and the lateral surface area of a cube of side 12 cm is:
Option 1: 292 cm2
Option 2: 290 cm2
Option 3: 288 cm2
Option 4: 286 cm2
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