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User AVIK DUTTA
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2 Answers

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ANSWER


4\pi - 8

Step-by-step explanation

The diagonal of the square can be found

using Pythagoras Theorem.


{d}^(2) = {(2 √(2) )}^(2) + {(2 √(2) )}^(2)


{d}^(2) = 4 * 2+ 4 * 2


{d}^(2) = 8+ 8


{d}^(2) = 16

Take positive square root


d = √(16) = 4

The radius is half the diagonal because the diagonal formed the diameter of the circle.

Hence r=2 units.

Area of circle is


\pi {r}^(2) =\pi * {2}^(2) = 4\pi

The area of the square is


{l}^(2) = {(2 √(2)) }^(2) = 4 * 2 = 8

The difference in area is


4\pi - 8

User Vdogsandman
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6 votes

Hello!

The answer is:

The difference between the circle and the square is:


Difference=4\pi -8

Why?

To solve the problem, we need to find the area of the circle and the area of the square, and then, subtract them.

For the square we have:


side=2√(2)

We can calculate the diagonal of a square using the following formula:


diagonal=side*√(2)

So,


diagonal=2√(2)*√(2)=2*(√(2))^(2)=2*2=4units

The area will be:


Area_(square)=side^(2)= (2√(2))^(2) =4*2=8units^(2)

For the circle we have:


radius=(4units)/(2)=2units

The area will be:


Area_(Circle)=\pi *radius^(2)=\pi *2^(2)=\pi *4=4\pi units^(2)


Area_(Circle)=4\pi units^(2)

Then, the difference will be:


Difference=Area_(Circle)-Area{Square}=4\pi -8

Have a nice day!

User Ben Souchet
by
6.1k points