The area of circle is equal to the area of square. The diagonal of square is 11 cm, then what will be the diameter of circle?
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Answers
Step-by-step explanation:
Area of square with diagonals 11 cm =>
=> 1/2d1d2 => 1/2 × 121 => 121/2 cm²
now area of circle = area of square which means
πr² = 121/2
=> 22/7 r² = 121/2
=> r² = 121/2 × 7/22
=> r² = 11/2×7/2
=> r²= 77/4
=> r = √77/2
=> d = 2r = 2×√77/2 = √77 cm
Answer:
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.