Subject: Compulsory Maths

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.

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

- Area of circle
- Circumference of circle

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

The area of a circle is 164 cm^{2}. Find its circumference.

Solution:

Area of a circle = 154 cm^{2}

So, \(\pi\)r^{2}= 154

or, r^{2}= \(\frac{154}{\pi}\)

or, r^{2}= \(\frac{154\times7}{22}\)

or, r^{2}= 49

or, r= \(\sqrt{49}\)

\(\therefore\) r =7cm

Find the circumference of a circle of radius 10.5 cm.

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

Find the diameter of a circle whose circumference is 88cm.

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

The diameter of a wheel of a van is 63cm. Find the distance travelled by the van during the period, the wheel makes revolutions.

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

The circumference of a circle is 44cm.Find its area.

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}

Find the circumference and area of radius 7cm.

Solution:

Circumference of circle = 2πr

= 2 × 22/7 × 7

= 44cm

Area of circle = πr^{2}

= 22/7 × 7 × 7 cm^{2}

= 154cm^{2}

The diameter of a circle is 6 yards. What is the circle's circumference?

Use 3.14 for π

Solution:

Given, Diameter (d) = 6 yards

π = 3.14

Now,

Circumference of a circle (c) = πd

= 3.14\(\times\)6

= 18.84yards

The diameter of a circle is 6 inches. What is the circle's radius?

Solution:

Given, Diameter(d) = 6inch

Now,

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

=\(\frac{1}{2}\)6

= 3inches

The radius of a circle is 1 mile. What is the circle's circumference?

Solution:

Given, Radius(r) = 1mile

π = 3.14

Now,

Circumference of circle (c) = 2πr

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

= 6.28miles

The radius of a circle is 3 millimeters. What is the circle's diameter?

Solution:

Given, radius (r) = 3millimeters

Now,

Diameter (d) = 2r

= 2\(\times\)3

= 6millimeters

The circumference of a circle is 6.28 miles. What is the circle's diameter?

Use 3.14 forπ

Solution:

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

π = 3.14

Now,

Radius (r) = \(\frac{c}{π}\)

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

= 2miles

The circumference of a circle is 3.14 miles. What is the circle's radius?

Use 3.14 for π

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

The radius of a circle is 4 millimeters. What is the circle's circumference?

Use 3.14 for π

Solution:

Given, Radius (r) = 4millimeters

π = 3.14

Now,

Circumference (c) = 2 π r

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

= 25.12millimeters

The radius of a circle is 10 millimeters. What is the circle's circumference?

Use 3.14 for π

Solution:

Given, Radius (r) = 10millimeters

π = 3.14

Now,

Circumference (c) = 2πr

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

= 62.8millimeters

The radius of a circle is 3 millimeters. What is the circle's circumference?

Use 3.14 for π

Solution:

Given, Radius (r) = 3millimeters

π = 3.14

Now,

Circumference (c) = 2πr

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

= 18.84millimeters

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