Question

Question 31

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

(a) $100c{m}^2$ (b) $200c{m}^2$
(c) $300c{m}^2$ (d) $400c{m}^2$

Answer 1

Given, radius of circle = 10 cm
The largest square that can be cut-out of a circle of radius 10 cm will have its diagonal equal to the diameter of the circle.
Let the side of a square be x.
Then, area of the square $=x\times x=x^{2}c{m}^2$ $[\because areaofsquare=(side{)}^2]$

Now, in right angled $\Delta DAB$,
$(BD{)}^2=(AD{)}^2+(AB{)}^2$ [by Pythagoras theorem]
$\because (20{)}^2=x^2+x^2$
$[\because diagonal=diameteranddiameter=2\times radius=2\times 10=20cm]$
$\Rightarrow 2x^2=400$
$\Rightarrow x^2=200$
$\therefore (Side{)}^2=200$
Hence, the area of the largest square is $200c{m}^2$