The area of a circle is the space occupied by the circle in a two-dimensional plane.
The formula for the area of a circle is
A = πr^{2}
where r is the radius of the circle.
The value of pie is 22/7 or 3.14.
Example 1 :
Find the area of a ring whose outer radius is 20 cm and inner radius is 15 cm respectively.
Solution :
Let "R" be the radius of the outer circle.
Ler "r" be the radius of the inner circle.
Area of outer circle = ΠR²
Area of outer circle = Πr²
Radius of outer circle (R) = 20 cm
Radius of the inner circle (r) = 15 cm
Area of ring (shaded portion)
= Area of outer circle - area of inner circle
= ΠR² - Πr²
= Π (R² - r²)
= Π (20² - 15²)
= Π x (400 - 225)
= Π x 175
= (22/7) x 175
= 22 x 25
= 550 cm²
Example 2 :
There is an outside circular path had constructed around a circular garden. If the outer and inner circumferences of the path are 88 cm and 44 cm respectively. Find the width and area of the path.
Solution :
Circumference of outer circle = 88
2ΠR = 88
2 x (22/7) x R = 88
R = (88 x 7) /(2 x 22)
R = 2 x 7
R = 14 cm
Circumference of inner circle = 44
2Πr = 44
2 x (22/7) x r = 44
R = (44 x 7) /(2 x 22)
R = (2 x 7)/2
R = 7 cm
Width of path = R - r
= 14 - 7
= 7 cm
Area of outer path = ΠR²
= (22/7) x 14²
= (22/7) x 14 x 14
= 616 cm²
Area of inner path = Πr²
= (22/7) x 7²
= (22/7) x 7 x 7
= 154 cm²
Area of path = 616 - 154
= 462 cm²
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