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The area of a 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 28.26 squares, the area of this circle would be 28.26 cm2.
Here is a way to find the formula for the area of a circle:
Cut a circle into equal sectors (16 in this example)
Rearrange the 16 sectors like this:
These sectors look like a rectangular region but not exactly so. The length of this rectangle will be equal to half of the circumference and breadth equal to the radius of the circle.
We know that:
Circumference = 2 × π × radius
And so the width is about:
Half the Circumference = π × radius
Now we just multply the width by the height to find the area of the rectangle:
Area = (π × radius) × (radius)
= π × radius2
Hence, we get
Area of the circle = \(\frac{1}{2}\) circumference x radius
= \(\frac{1}{2}\) x 2\(\pi\)r x r^{2}
= \(\pi\)r^{2}
Verification:
Draw three circles of different radii. Measure the diameter of each one of them with the help of scale andfill teh table given below:
Circle | Radius(r) | Diameter(2r) | Circumference(c) | \(\frac{Circumference}{Diameter}\)=\(\frac{c}{2r}\) |
(i) | ||||
(ii) | ||||
(iii) |
The ratio is denoted bycalled pi (\(\pi\))
Here,
\(\pi\) = 3.14(nearly)
= \(\frac{22}{7}\) (nearly)
Thus,
\(\frac{Circumference}{Diameter}\) = \(\pi\)
or, \(\frac{c}{2r}\) = \(\pi\)
or, c = 2\(\pi\)r
\(\therefore\) Circumference of a circle(c) = 2\(\pi\)r
Soution:
The circumference of the circle is given by
c =2\(\pi\)r
=2\(\times\)\(\frac{22}{7}\)\(\times\)10.5
=66 cm
Thus, circumference=66 cm
Solution:
We know that, c=2\(\pi\)r
or, 88=2\(\times\)\(\frac{22}{7}\)\(\times\)r
or, r=\(\frac{88\times7}{2\times22}\)\(\times\)r
or, r=\(\frac{88 x 7 }{2 x 22}\)
\(\therefore\) r=14cm
Thus, radius=14cm
Solutions:
Note that, in 1 revolution the car covers a distance equal to the circumference of the wheel.
Now, the diameter of the wheel=63 cm
Therefore, radius(r)=\(\frac{63}{2}\)cm
Circumference of the wheel= 2\(\pi\)r
=2\(\times\)\(\frac{22}{7}\)\(\times\)\(\frac{63}{2}\)
=198cm
=1.98m
Here, the distance covered in 1 revolution=1.98 m
Distance covered in 1000 revolutions=1.98\(\times\)1000
=1980m
Solution:
Circumference= 44 cm
So, 2\(\pi\)r=44
or, r=\(\frac{44}{2\pi}\)
or, r=\(\frac{44\times7}{2\times22}\)
\(\therefore\) r=7cm
Area of the circle=\(\pi\)r^{2}
=\(\frac{22}{7}\)\(\times\)7 \(\times\)7
=154cm^{2}
Solution:
Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44cm
Area of circle = πr^{2}
= 22/7 × 7 × 7 cm^{2}
= 154cm^{2}
Solution:
Given, Diameter (d) = 6 yards
π = 3.14
Now,
Circumference of a circle (c) = πd
= 3.14\(\times\)6
= 18.84yards
Solution:
Given, Diameter(d) = 6inch
Now,
Radius (r) = \(\frac{1}{2}\)d
=\(\frac{1}{2}\)6
= 3inches
Solution:
Given, Radius(r) = 1mile
π = 3.14
Now,
Circumference of circle (c) = 2πr
= 2\(\times\)3.14\(\times\)1
= 6.28miles
Solution:
Given, radius (r) = 3millimeters
Now,
Diameter (d) = 2r
= 2\(\times\)3
= 6millimeters
Solution:
Given, Circumference of a circle (c) = 6.28miles
π = 3.14
Now,
Radius (r) = \(\frac{c}{π}\)
= \(\frac{6.28}{3.14}\)
= 2miles
Solution:
Given, Circumference of a circle (c) = 6.28miles
π = 3.14
Now,
Radius (r) = \(\frac{c}{2π}\)
= \(\frac{3.14}{2\times3.14}\)
= 5miles
Solution:
Given, Radius (r) = 4millimeters
π = 3.14
Now,
Circumference (c) = 2 π r
= 2\(\times\)3.14\(\times\)4
= 25.12millimeters
Solution:
Given, Radius (r) = 10millimeters
π = 3.14
Now,
Circumference (c) = 2πr
= 2\(\times\)3.14\(\times\)10
= 62.8millimeters
Solution:
Given, Radius (r) = 3millimeters
π = 3.14
Now,
Circumference (c) = 2πr
= 2\(\times\)3.14\(\times\)3
= 18.84millimeters
ASK ANY QUESTION ON Area and Circumference of a Circle
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Drishya
If the circumference of a circular stadium is 88 m , find the area of stadium
Mar 19, 2017
1 Replies
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