FIND THE CIRCUMFERENCE OF THE CIRCLE

What is circumference of the circle ?

The meaning of circumference is the distance around a circle or any curved geometrical shape.

It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.

The formula for the circumference of the circle (C) is

C = 2πr

(where r is the radius of the circle)

Find the circumference of each circle in terms of π.

Problem 1 :

Solution :

The formula for the circumference of the circle is

= 2πr

Here (r) = 5 in

= 2 × π × 5

= 10π in

So, the circumference of the given circle is about 10π in.

Problem 2 :

Solution :

Formula for circumference of circle is

= 2πr

Here (r) = 8 ft

= 2 × π × 8

= 16π ft

So, the circumference of the given circle is about 16π ft.

Problem 3 :

Solution :

Formula for circumference of circle is

= 2πr

Here (r) = 15 yd

= 2 × π × 15

= 30π yd

So, the circumference of the given circle is about 30π yd.

Problem 4 :

Solution :

C = 2πr

Here (r) = 10 yd

= 2 × π × 10

= 20π yd

So, the circumference of the given circle is about 20π yd.

Problem 5 :

Solution :

C = 2πr

Here (r) = 7 in

= 2 × π × 7

= 14π in

So, the circumference of the given circle is about 14π in.

Problem 6 :

Solution :

C = 2πr

Here (r) = 2 ft

= 2 × π × 2

= 4π ft

So, the circumference of the given circle is about 4π ft.

Problem 7 :

Solution :

C = 2πr

Here (r) = 16 ft

= 2 × π × 16

= 32π ft

So, the circumference of the given circle is about 32π ft.

Problem 8 :

Solution :

C = 2πr

Here (r) = 4 yd

= 2 × π × 4

= 8π yd

So, the circumference of the given circle is about 8π yd.

Problem 9 :

Solution :

C = 2πr

Here (r) =12 in

= 2 × π × 12

= 24π in

So, the circumference of the given circle is about 24π in.

Problem 10 :

The circumference of the roll of caution tape decreases 10.5 inches after a construction worker uses some of the tape. Which is the best estimate of the diameter of the roll after the decrease? 

a)  5 inches    b)  7 inches   c)  10 inches      d)  12 inches

Solution :

After the decrease, the circumference of the roll is 31.4 − 10.5 = 20.9 inches.

C = πd

20.9 = 3.14(d)

d = 20.9/3.14

d = 6.65 inches

= 7 inches

So, option b is correct.

Problem 11 :

A semicircle is one-half of a circle. Find the perimeter of the semicircular region.

Solution :

The straight side is 6 meters long. The distance around the curved part is one-half the circumference of a circle with a diameter of 6 meters.

Perimter of semicircle = πd/2 + 2r

= 3.14(6)/2 + 6

= 3.14(3) + 6

= 9.42 + 6

= 15.42 m

Problem 12 :

A circular sinkhole has a circumference of 75.36 meters. A week later, it has a circumference of 150.42 meters.

a. Estimate the diameter of the sinkhole each week.

b. How many times greater is the diameter of the sinkhole now compared to the previous week?

Solution :

a)

Circumference of the sinkhole one week earlier = 75.36 m

πd = 75.36

3.14 d = 75.36

d = 75.36/3.14

d = 24 m

Circumference of the sinkhole one week later = 150.42 m

πd = 150.42

3.14 d = 150.42

d = 150.42/3.14

d = 47.9

Approximately 48 m.

b)

number of times = 48/24

= 2 times

Problem 13 :

Find the circumference of circles :

Solution :

Circumference of yellow circle = 2πr

r = 5 cm

= 2 (3.14) (5)

= 10(3.14)

= 31.4 cm

Cricumference of blue circle = 2πR

R = 5 + 5 ==> 10 cm

= 2 (3.14) (10)

= 20(3.14)

= 62.8 cm

Problem 14 :

The length of the minute hand is 150% of the length of the hour hand.

a. What distance will the tip of the minute hand move in 45 minutes?

Explain how you found your answer.

Solution :

Length of hour hand = 36 mm

Length of minute hand = 150% of 36

= 1.50(36)

= 54 mm

Angle measure created to have 45 minutes

= Length of curve of semicircle + length of curve of quadrant 

= (3/4) 2πr 

= (3/4) 2πr 

= (3/4) x 2 x 3.14 x 54

= 254.34 mm