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प्रश्न
In Figure 4, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)
उत्तर
ABCD is a square. A quadrant of circle of radius 1 cm is drawn at each vertex of the square.
The quadrant of a circle is a sector of angle 90°.
`\text{Area of each quadrant) =` `pi90^@/360^@=(r^2)3=1_1^4,4xx(1cm) 0.785 cm`
Area of square = (Side)2 = (4 cm)2 = 16 cm2
Diameter of the circle = 2 cm
∴ Radius of the circle = 1 cm
∴ Area of circle = πr2 = 3.14 × (1 cm)2 = 3.14 cm2
Area of shaded region
= Area of square − Area of circle − (4 × Area of each quadrant)
= 16 cm2 − 3.14 cm2 − (4 × 0.785 cm2)
= 16 cm2 − 3.14 cm2 − 3.14 cm2
= 16 cm2 − 6.28 cm2
= 9.72 cm2
Thus, the area of the shaded region is 9.72 cm2.
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