Area of circle

The Area of circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm², you could count the total number of squares to get the area of this circle. Thus, if there were a total of 17 squares, the area of this circle would be 17 cm² However, it is easier to use one of the following formulas:
The region inside the circle is called its area. The formula to find the area is Area = π x r²; where the value of π is taken as either 3.14 or 22 / 7.
The unit of area is m² or cm².
Some solved examples
1) Find the area of a circle of radius 4.2 cm.
Solution : Area of circle = π x r²
Area = 3.14 x (4.2)²
= 55.44 cm²
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2) A copper wire, when bent in the form of a square, encloses an area of 484 cm². If the same wire is bent in the form of a circle, find the area enclosed by it.
Solution : Area of square = 484 cm²
⇒ (side )² = 22²
⇒ 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 r² = 3.14 x 14²
Area = 616 cm²
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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.

Solution : PS = 12 cm
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 6² + 3.14 x 2² - 3.14 x 4²]
= 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 cm²
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Mensuration : Area and Perimeter

• Circumference of Circle
• Area of Circle
Mensuration

7th grade math

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