Question

Given that the area of a square inscribed in a circle is 64 cm^2, how do you find the area of the circle?

Answer 1

area of the circle `=color(purple)( 100.48 cm^2`

Explanation:

Area of the square `= 64cm^2`
So the side of this square `=color(purple)( sqrt64 = 8cm`
And the diagonal of this square `= sidesqrt2 =color(purple)( 8sqrt2`

Given that the square is inscribed inside the circle , the diagonal of this square `=` the diameter `(d)` of the circle.

`color(purple)(8sqrt2) = d`
So, the radius , `color(purple)(r = 4sqrt2`

Now , the area of the circle `= pi(r)^2`
`= 3.14 xx color(purple)((4sqrt2)^2`
`= 3.14 xx color(purple)(16 xx 2`

`=color(purple)( 100.48 cm^2`