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The region inside the circle is called its area. The formula to find the area is Area = π x r

The unit of area is m

1) Find the area of a circle of radius 4.2 cm.

Area = 3.14 x (4.2)

= 55.44 cm

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2) A copper wire, when bent in the form of a square, encloses an area of 484 cm

⇒ (side )

⇒ Side = 22 cm

So, the perimeter of square = 4 x side = 4 x 22 = 88 cm

Circumference of a circle = Perimeter of square

⇒ 2 x π x r = 88

⇒ 2 x 3.14 x r = 88

⇒ r = 14 cm

Area of circle = π x r

Area = 616 cm

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3) PQRS is a diameter of a circle of radius 6 cm. The lengths PQ,QR and RS are equal. Semicircles are drawn on PQ and QS as diameters.Find the area of the shaded region.

As PQ = QR =RS

∴ PQ =QR =RS = 1/3 x PS = 1/3 x 12 = 4 cm.

QS = 2 PQ

QS = 2 x 4 = 8 cm

∴ Area of shaded region = Area of semicircle with PS as diameter + Area of semicircle with PQ as diameter – Area of semicircle with QS as diameter.

= ½ [ 3.14 x 6

= ½ [ 3.14 x 36 + 3.14 x 4 – 3.14 x 16 ]

= ½ [ 3.14 ( 36 + 4 – 16)]

= ½ ( 3.14 x 24 ) = ½ x 75.36

∴ Area of shaded region = 37.68 cm

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• Circumference of Circle

• Area of Circle

7th grade math

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