Question

. What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

Answer 1

From the question it is given that, radius of circle 10 cm.

Square has diagonal equal to its diameter.

Diameter = 2 × radius

= 2 × 10

= 20 cm

Then, let us assume the side of the square be P.

So, area of square be P2.

By the rule of Pythagoras theorem,

Diagonal2 = height2 + base2

202 = P2 + P2

202 = 2P2

400 = 2P2

P2 = 400/2

P2 = 200 cm2

Therefore, area the largest square that can be cut out of a circle of radius 10 cm is 200 cm2.

Hope it helps...... ❣️

Answer 2

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Each diagonal of this large square=diameter of circle = 20 cm.

These diagonals intersect at 90° on point O(centre of the circle)

Let ABCD is that square having each side x cm., diagonalsAC=BD=20 cm

AO=AC/2=20/2=10 cm. , BO=BD/2=20/2=10 cm.

In right angled triangle AOB :- AO^2+BO^2=A B^2

(10)^2+(10)^2=x^2 , 200=x^2 ……………(1)

Area of large square= side^2= x^2=200 sq. cm. [ From eq.(1) put x^2=200 ] ,Answer.