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  • The side of a square is 10 cm. Find the area between inscribed and circumscribed circles of the square.       <div style="float:left;

The side of a square is 10 cm. Find the area between inscribed and circumscribed circles of the square.

 

 
 
 
 
 

Answers (1)

The side of the square is 10 cm 

using Pythagoras theorem 

d = \sqrt { 10 ^2 + 10 ^ 2} = 10 \sqrt 2

The radius of inscribed 5 cm the radius of the circumscribed circle is 5\sqrt 2 The area of between inscribed and circumscribed circles of the square is 

A = \pi R^2 - \pi r ^2 \\\\ A = \pi ( 5\sqrt 2 )^2 - \pi \times 5^2 \\\\ A = \pi \times 50 - \pi \times 25 \\\\ = \pi ( 50 -25 ) \\\\ A = 25 \pi

Therefore the area between inscribed and circumscribed circles of the square is 25 \pi cm^2

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Safeer PP

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