Question

the area of circle that can be in described in a square of side 10 cm is​

Answer 1

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

Hint: Use the information, for inscribed circle: radius =side of square2⇒r1=102=5cm and for circumscribed circle: diameter of the circle = diagonal of the square. Also, the area between these circles is nothing but the difference of their area.

Complete step-by-step answer:

For inscribed circle: radius=side of square2⇒r1=102=5cm.

We know that, area of the circle is given by πr2.

So, the area of the inscribed circle is πr12=π×52=25πcm2.

For circumscribed circle: diameter of the circle = diagonal of the square.

We can use Pythagoras theorem to find the length of the diagonal of the square.

(diagonal)2=102+102=2×100⇒diagonal=102–√cm.

Then, radius =diagonal2⇒r2=102–√2=52–√cm.

Now, again we can use the formula of area of the circle for circumscribed circle which is πr22=π×(52–√)2=50πcm2.

Now, the area between these circles is nothing but the difference of their area which is 50π−25π=25πcm2≈78.511cm2.

Answer 2

Answer:

side of the square is 10CM

thus diameter of the circle inscribed

in a square id 10CM

d=10CM

thus area of the circle is given by

A=r/4×d2

A=r/4×(10)2

A=r/4×100

A=25r CM2

Thank you