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 cm 2
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$
$= 2×\frac{22}{7}×( \frac{7}{2})^2$
$= 77$ cm
2
Hence, the correct answer is 77 cm
2
.
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