Notes on Area and Circumference of a Circle | Grade 8 > Compulsory Maths > Area and Perimeter of Plain Figures | KULLABS.COM

Area and Circumference of a Circle

Notes, Exercises, Videos, Tests and Things to Remember on Area and Circumference of a Circle

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  • Note
  • Things to remember
  • Exercise

Area of a Circle

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 r2

= \(\pi\)r2

Circumference of a Circle



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) \(\frac{Circumference}{Diameter}\)=\(\frac{c}{2r}\)

The ratio is denoted bycalled pi (\(\pi\))


\(\pi\) = 3.14(nearly)

= \(\frac{22}{7}\) (nearly)


\(\frac{Circumference}{Diameter}\) = \(\pi\)

or, \(\frac{c}{2r}\) = \(\pi\)

or, c = 2\(\pi\)r

\(\therefore\) Circumference of a circle(c) = 2\(\pi\)r

  • Area of circle 
  • Circumference of circle 

Questions and Answers

Click on the questions below to reveal the answers


The circumference of the circle is given by

c =2\(\pi\)r


=66 cm

Thus, circumference=66 cm


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


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




Here, the distance covered in 1 revolution=1.98 m

Distance covered in 1000 revolutions=1.98\(\times\)1000



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=\(\pi\)r2

=\(\frac{22}{7}\)\(\times\)7 \(\times\)7



Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44cm

Area of circle = πr2
= 22/7 × 7 × 7 cm2
= 154cm2


Given, Diameter (d) = 6 yards

π = 3.14


Circumference of a circle (c) = πd

= 3.14\(\times\)6

= 18.84yards


Given, Diameter(d) = 6inch


Radius (r) = \(\frac{1}{2}\)d


= 3inches


Given, Radius(r) = 1mile

π = 3.14


Circumference of circle (c) = 2πr

= 2\(\times\)3.14\(\times\)1

= 6.28miles


Given, radius (r) = 3millimeters


Diameter (d) = 2r

= 2\(\times\)3

= 6millimeters


Given, Circumference of a circle (c) = 6.28miles

π = 3.14


Radius (r) = \(\frac{c}{π}\)

= \(\frac{6.28}{3.14}\)

= 2miles


Given, Circumference of a circle (c) = 6.28miles

π = 3.14


Radius (r) = \(\frac{c}{2π}\)

= \(\frac{3.14}{2\times3.14}\)

= 5miles


Given, Radius (r) = 4millimeters

π = 3.14


Circumference (c) = 2 π r

= 2\(\times\)3.14\(\times\)4

= 25.12millimeters


Given, Radius (r) = 10millimeters

π = 3.14


Circumference (c) = 2πr

= 2\(\times\)3.14\(\times\)10

= 62.8millimeters


Given, Radius (r) = 3millimeters

π = 3.14


Circumference (c) = 2πr

= 2\(\times\)3.14\(\times\)3

= 18.84millimeters


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