AREA AROUND CIRCLE

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  =  πr2

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

Related Pages

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