Moon's crescent is formed when Earth's shadow is cast on it. If a full moon appears as a circle of radius 5cm to the naked eye and Earth's shadow appears as a circle of radius 3cm, find the area of the crescent. (Consider that Earth's shadow lies completely inside the Moon.)

4π sq.cm

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8π sq.cm

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16π sq.cm

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32π sq.cm

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Solution

The correct option is C 16π sq.cm
The given image shows that Earth's shadow lies completely inside the Moon.

Now, for the naked eye:

$M o o n^{'} s r a d i u s = 5 c m$

$⟹ M o o n^{'} s a r e a = π \times 5^{2} = 25 π s q . c m$

Also,

$R a d i u s o f E a r t h^{'} s s h a d o w = 3 c m$

$⟹ A r e a o f E a r t h^{'} s s h a d o w = π \times 3^{2} = 9 π s q . c m$

Hence,

$A r e a o f M o o n^{'} s c r e s c e n t = 25 π - 9 π = 16 π s q . c m$

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