The Circumference And Area Of Circle

(1). Given: Diameter = 3.5 cm

⇒ Radius, r = Diameter/2

⇒ r = 3.5/2 = 1.75 cm

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 11 cm.

(2). Given: Diameter = 6.3 m

⇒ Radius, r = Diameter/2

⇒ r = 6.3/2 = 3.15 m

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 19.8 cm.

(3). Given: Diameter = 0.14 m

⇒ Radius, r = Diameter/2

⇒ r = 0.14/2 = 0.07 m

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 0.44 m.

(1). Given: Radius, r = 56 cm

We have

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 352 cm.

(2). Given: Radius, r = 7.7 cm

We have

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 48.4 cm.

(3). Given: Radius, r = 2.8 m

We have

Circumference of the circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

Hence, circumference is 17.6 m.

(1). Given: Circumference = 198 cm

And we know circumference of a circle is given by,

Circumference = 2πr

⇒

Substituting Circumference = 198 cm and π = 22/7,

⇒

⇒

If radius, r = 31.5 cm

Then diameter = 2r

⇒ diameter = 2 × 31.5 = 63

We can draw the circle as

Hence, radius is 31.5 cm and diameter is 63 cm.

(2). Given: Circumference = 616 cm

And we know circumference of a circle is given by,

Circumference = 2πr

⇒

Substituting Circumference = 616 cm and π = 22/7,

⇒

⇒

If radius, r = 98 cm

Then diameter = 2r

⇒ diameter = 2 × 98 = 196

We can draw the circle as

Hence, radius is 98 cm and diameter is 196 cm.

(3). Given: Circumference = 72.6 m

And we know circumference of a circle is given by,

Circumference = 2πr

⇒

Substituting Circumference = 72.6 m and π = 22/7,

⇒

⇒

If radius, r = 11.55 cm

Then diameter = 2r

⇒ diameter = 2 × 11.55 = 23.1

We can draw the circle as

Hence, radius is 11.55 m and diameter is 23.1 m.

We have

Given: Radius of the circular fence, r = 7.7 m

The wire is about the circular fence. So, we need to find the circumference of this circular fence in order to find the length of the wire used in 1 round of fence.

Circumference of circle is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

If the circumference of the circular fence = 48.4 m

Then, length of wire used in 1 round = 48.4 m

⇒ length of wire used in 3 rounds = 3 × 48.4

= 145.2 m

If the cost of 1 m of wire used = Rs. 50

Then, cost of 145.2 m of wire used = 50 × 145.2

= 7260

Thus, cost of fencing the circular place with 3 rounds of wire is Rs. 7260.

Given: Diameter of the wheels of the bus = 0.7 m

⇒ Radius of the wheels of the bus, r = diameter/2 = 0.7/2 = 0.35 m

⇒ r = 0.35 m

We have

We need to find circumference of the wheels that will tell us about the distance it covers in 1 rotation.

Circumference of a circular wheel is given by,

Circumference = 2πr

⇒ Circumference

⇒ Circumference

If the circumference of the wheel = 2.2 m

Then, distance covered by the wheel in 1 rotation = 2.2 m

We know, 1 m = 0.001 km

⇒ 2.2 m = 2.2 × 0.001 = 2.2 × 10^-3 km

⇒ distance covered by the wheel in 1 rotation = 2.2 × 10^-3 km

Or

Rotations covered in 2.2 × 10^-3 km = 1

⇒ Rotations covered in 1 km = 1/(2.2 × 10^-3)

⇒ Rotations covered in 22 km = 22/(2.2 × 10^-3) = 10000

Thus, the wheels of the bus rotate 10,000 times for covering a distance of 22 km between two towns.

(1). We have been given: radius = 42 cm

We need to find: diameter = ?, circumference = ? and area = ?

We have

To find diameter:

Diameter = 2 × radius

⇒ diameter = 2 × 42 = 84 cm

To find circumference:

Circumference = 2πr, where r = radius

⇒ Circumference

⇒ Circumference

To find area:

Area = πr², where r = radius

⇒ Area

⇒ Area

Thus, diameter = 84 cm, circumference = 264 cm & area = 5544 cm².

(2). Given: diameter = 9.8 m

We need to find: radius = ?, circumference = ? & area = ?

We have

To find radius:

Radius = diameter/2

⇒ radius = 9.8/2 = 4.9 m

To find circumference:

Circumference = 2πr, where r = radius

⇒ Circumference

⇒ Circumference

To find area:

Area = πr², where r = radius

⇒ Area

⇒ Area

Thus, diameter = 4.9 m, circumference = 30.8 m & area = 75.46 m².

(3). Given: circumference = 44 m

We need to find: radius = ?, diameter = ? & area = ?

To find radius:

If circumference = 44 m

⇒ 2πr = 44 [∵, circumference of circle = 2πr, where r = radius]

⇒

⇒

⇒

⇒ radius = 7 m …(i)

To find diameter:

Diameter = 2 × radius

⇒ diameter = 2 × 7 = 14 m [from (i)]

To find area:

Area = πr²

⇒ [from (i)]

⇒ Area = 22 × 7 = 154 m²

Thus, radius = 7 m, diameter = 14 m & area = 154 m².

(4). Given: area = 616 cm²

We need to find: radius = ?, diameter = ? & circumference = ?

To find radius:

If area = 616 cm²

⇒ πr² = 616 [∵, area of circle = πr², where r = radius]

⇒

⇒

⇒

⇒ r = √196 = 14 cm …(i)

To find diameter:

Diameter = 2 × radius

⇒ diameter = 2 × 14 = 28 cm

To find circumference:

Circumference = 2πr, where r = radius

⇒ Circumference

⇒ Circumference

Thus, radius = 14 cm, diameter = 28 cm and circumference = 88 cm.

(1). Given: radius, r = 28 cm

We have

Area is given by,

Area = πr²

⇒ Area

⇒ Area

⇒ Area

Thus, area of the circle is 2464 cm².

(2). Given: radius, r = 5.6 m

We have

Area is given by,

Area = πr²

⇒ Area

⇒ Area

⇒ Area

Thus, area of the circle is 98.56 m².

(3). Given: radius, r = 7.7 m

We have

Area is given by,

Area = πr²

⇒ Area

⇒ Area

⇒ Area

Thus, area of the circle is 186.34 m².

(4). Given: radius, r = 6.3 m

We have

Area is given by,

Area = πr²

⇒ Area

⇒ Area

⇒ Area

Thus, area of the circle is 124.74 m².

(5). Given: radius, r = 35 cm

We have

Area is given by,

Area = πr²

⇒ Area

⇒ Area

⇒ Area

Thus, area of the circle is 3850 cm².

(1). Given: Area of circle = 1386 cm²

To find diameter:

We know that, area is given by

Area = πr²

⇒ r² = Area/π

⇒

⇒

⇒ r = √441

⇒ r = 21

If radius, r = 21 cm

Then, diameter = 2r = 2 × 21

⇒ diameter = 42

Thus, diameter is 42 cm.

(2). Given: Area of the circle = 346.5 cm²

To find diameter:

We know that, area is given by

Area = πr²

⇒ r² = Area/π

⇒

⇒

⇒ r = √110.25

⇒ r = 10.5

If radius, r = 10.5 cm

Then, diameter = 2r = 2 × 10.5

⇒ diameter = 21

Thus, diameter is 21 cm.

(3). Given: Area of the circle = 3850 m²

To find diameter:

We know that, area is given by

Area = πr²

⇒ r² = Area/π

⇒

⇒

⇒ r = √1225

⇒ r = 35

If radius, r = 35 m

Then, diameter = 2r = 2 × 35

⇒ diameter = 70

Thus, diameter is 70 m.

(4). Given: Area of the circle = 301.84 m²

To find diameter:

We know that, area is given by

Area = πr²

⇒ r² = Area/π

⇒

⇒

⇒ r = √96.04

⇒ r = 9.8

If radius, r = 9.8 m

Then, diameter = 2r = 2 × 9.8

⇒ diameter = 19.6

Thus, diameter is 19.6 m.

(5). Given: Area of the circle = 24.64 m²

To find diameter:

We know that, area is given by

Area = πr²

⇒ r² = Area/π

⇒

⇒

⇒ r = √7.84

⇒ r = 2.8

If radius, r = 2.8 m

Then, diameter = 2r = 2 × 2.8

⇒ diameter = 5.6

Thus, diameter is 5.6 m.

Given: circumference of the circle = 96.8 m

And we know circumference of a circle is given by

Circumference = 2πr, where r = radius of the circle

⇒ r = circumference/2π

⇒

⇒

⇒ radius = 15.4 m

To find area of this circle:

Area is given by

Area = πr²

⇒ Area = 22/7 × 15.4²

⇒ Area = (22 × 15.4 × 15.4)/7

⇒ Area = 5217.52/7 = 745.36 m²

Thus, area of circle is 745.36 m².

Given: AB = 14 cm & AM = MB

Clearly, AB = AM + MB

⇒ AB = AM + AM = 2 AM

⇒ AM = AB/2

⇒ AM = 14/2 = 7 cm

Also, area of circle is given by

Area = πr²

Area of semicircle = πr²/2

Now, if diameter of one of the semicircle = 7 cm

Then, radius of that semicircle = 7/2 = 3.5 cm

So, area of that semicircle

…(i)

Radius of the other semicircle = 7/2 = 3.5 cm

So, area of that other semicircle

…(ii)

Adding equations (i) and (ii), we get

Total area of the shaded part = 19.25 + 19.25

= 38.5 cm

Thus, total area of the shaded part is 38.5 cm².

Alternate Method:

Given that AB = 14 cm & AM = MB

Notice, AB = AM + MB

⇒ AB = AM + AM

⇒ AB = 2 AM

⇒ AM = AB/2

⇒ AM = 14/2 = 7 cm

So, if AM is joined with MB, then it forms a complete circle of diameter, 7 cm.

Then, radius of this circle = 7/2 = 3.5 cm

When points A and B are met together, they form a circle.

Let AB = L and center of this circle = O.

Then, we have LM = 7 cm and LO = OM = 3.5 cm (radius).

Area of this circle is given by

Area = πr²

⇒ Area = 22/7 × 3.5²

⇒ Area = (22 × 3.5 × 3.5)/7

⇒ Area = 269.5/7 = 38.5 cm²

Thus, total area of the shaded part is 38.5 cm².

Given that, radius of the circular lid of a tank, r = 1.4 m

Now this lid is painted on both sides. So, we need to find area of both sides of the circular lid.

Area of one side = πr²

= 22/7 × 1.4²

= (22 × 1.4 × 1.4)/7

= 43.12/7

= 6.16

Area of both sides = 2 × Area of one side

= 2 × 6.16

= 12.32

So, area painted on both sides of 1 circular lid = 12.32 m²

Then, area painted on both sides of 100 such circular lid = 12.32 × 100 = 1232 m²

Cost of painting 1 m² area = Rs. 20

Cost of painting 1232 m² area = 20 × 1232 = Rs. 24640

Thus, it will cost Rs. 24,640 to paint 100 such lids at the rate of Rs. 20 per m².