Question 102

The diameter of a circle is equal to the diagonal of a square whose area is 784 m 2 . What is the area of the circle ? (In m 2 )

Solution

Let side of square = $$a$$ m

=> Area of square = $$a^2 = 784$$

=> $$a = \sqrt{784} = 28$$ m

=> Diagonal of square = $$\sqrt{28^2 + 28^2} = 28 \sqrt{2}$$ m = Diameter of circle

=> Radius of circle = $$\frac{28 \sqrt{2}}{2} = 14 \sqrt{2}$$ m

$$\therefore$$ Area of circle = $$\pi r^2$$

= $$\frac{22}{7} (14 \sqrt{2})^2 = 22 \times 28 \times 2$$

= $$1232 m^2$$

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