Question

A circle has same area as that of the square of diagonal of length 11.0 cm. What is the diameter of the circle?


Answer comes to be 8. 7cm
Plz help me ​

Answer 1

Answer:

so diameter is 8.7cm.

hope it is useful!!!!!!

Answer 2

Given:

• A circle has same area as that of square of diagonal 11cm.

To Find:

• The value of diameter of the circle.

Answer:

Its given that a square and a circle have equal area and measure of diagonal of square is 11cm.

Now area of square in terms of diagonal is given by , ½ × (diagonal)².

Now how do we get this ?

Already we know that the area of square is equal to (side)² and the angle between the two sides is 90° .

So , when we join diagonal to two sides , it forms a right angled ∆.

Let each side be x and diagonal be d .

Just apply Pythagoras Theorem now ,

=> (hypotenuse)²=(perpendicular)²+(base)².

=> d² = a² + a² .

=> d² = 2a².

=> d = √2a².

=> d = √2a.

=> a = d/√2.

Hence the area becomes

= (a)² = (d/√2)² = 1/2 × d².

Therefore area of square

= 1/2 × 11 × 11 cm².

= 121/2cm².

= 60.5cm².

And area of square is πr² , where r is radius.

=> πr² = 60.5cm²

=> 3.14 × r² = 60.5 cm²

=> r² = 60cm²/3.14.

=>r² = 19.26.

=> r = √19.26

=> r = 4.38.

Hence diameter = 2r = 2× 4.38 = 8.76cm ≈ 8.7cm.

Hence the diameter is 8.7cm.