Area of Circle


 
 
Concept Explanation
 

Area of Circle

Area of A Circle:

The area enclosed by a circle of radius r is large pi r^2. Here the Greek letter π represents a constant, approximately equal to 3.14159, which is equal to the ratio of the circumference of any circle to its diameter.

Area ;of;circle = pi r^2

Illustration: Find the area of circle whose radius is 7cm

Solution: Radius  r= 7 cm

Area ;of;circle = pi r^2   = frac{22}{7}X;7;X;7 =  154 sq.cm.

 

Illustration: The figure shows two circles with the same center. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.

Find:

(a) the area of the larger circle 

(b) the area of the smaller circle   

(c) the shaded area between the two circles. large (pi =3.14)

Solution: According to the question

(a) Radius of the larger circle = 10 cm, 

So, area of the larger circle = large pi r^{2}  =3.14times10times10times=314;cm^{2}

(b) Radius of the smaller circle = 4 cm,  

Area of the smaller circle = large pi r^{2}  =3.14times4times4=50.24;cm^{2}

(c) Area of the shaded region =  Area of Larger Circle - Area of Smaller Circle

=(314-50.24)cm^{2}=263.76;cm^{2}

Illustration:  A path of width 2m runs around a circular park whose circumference  dpi{110} 75frac{3}{7} m. Find the area of the path.

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Sample Questions
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Question : 1

When the circumference and area of a circle are numerically equal, then the diameter is numerically equal to:

Right Option : D
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Explanation
Question : 2

A wire bent in the form of a circle of radius 42 cm is cut and again bent in the form of a square. The ratio of the regions enclosed by the circle and the square in the two cases is given by:

Right Option : D
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Explanation
Question : 3

A circular disc of area 0.49pi sq.meters rolls down a length of 1.76 kms. The number of revolution it makes is

Right Option : B
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Explanation
 
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