In the diagram, the circle has centre O and square OPQR has vertex Q on the circle. If the areaof the circle is72 sq. units , the area of the square is
Question
In the diagram, the circle has centre O and square OPQR has vertex Q on the circle. If the areaof the circle is72 sq. units , the area of the square is
Solution
The area of a circle is given by the formula πr², where r is the radius of the circle. Given that the area of the circle is 72π square units, we can set up the equation:
πr² = 72π
Dividing both sides by π, we get:
r² = 72
Taking the square root of both sides, we find that the radius r is √72 units.
In the given diagram, the radius of the circle is also the side length of the square OPQR. Therefore, the area of the square is given by the formula s², where s is the side length of the square.
Substituting √72 for s, we get:
Area of square = (√72)² = 72 square units.
So, the area of the square OPQR is 72 square units.
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