#### Solved Examples and Worksheet for Circumference of Circles

Q1Find the circumference of a basketball hoop if it has a diameter of 24 cm. [Use π = 3.14.]
A. 75.36 cm
B. 27.14 cm
C. 7.64 cm
D. 150.72 cm

Step: 1
The circumference of a circle = π × diameter.
[Formula.]
Step: 2
= 3.14 × 24
[Substitute π = 3.14 and diameter = 24 cm.]
Step: 3
= 75.36 cm.
[Simplify.]
Step: 4
The circumference of the basketball hoop is 75.36 cm.
Correct Answer is :   75.36 cm
Q2What is the circumference of a circle with diameter 21 inches? [Use π = 3.14.]
A. 72.94 inches
B. 75.94 inches
C. 65.94 inches
D. 131.88 inches

Step: 1
The diameter of the circle is 21 inches.
[Given.]
Step: 2
The circumference of a circle = π × diameter.
[Formula.]
Step: 3
The circumference of the circle = 3.14 × 21.
[Substitute π = 3.14 and diameter = 21 inches.]
Step: 4
= 65.94 inches
Step: 5
The circumference of the circle is 65.94 inches.
Correct Answer is :   65.94 inches
Q3Find the circumference of a circle whose radius is 48 cm. [Use π = 3.14.]

A. 311.44 cm
B. 602.88 cm
C. 150.72 cm
D. 301.44 cm

Step: 1
The radius (r) of the circle is 48 cm.
[Given.]
Step: 2
The circumference of the circle = 2 × π × r
[Formula.]
Step: 3
= 2 × 3.14 × 48
[Substitute π = 3.14 and r = 48 cm.]
Step: 4
= 301.44 cm
[Simplify.]
Step: 5
The circumference of the circle is 301.44 cm.
Correct Answer is :   301.44 cm
Q4The circumference of a circle is 2πr. Find the circumference of the circle, when the radius r is equal to 5.

A. 9π
B. 11π
C. 12π
D. 10π

Step: 1
Evaluate 2πr for r = 5
Step: 2
2πr = 2π(5)
[Substitute r for 5.]
Step: 3
= 10π
[Multiply.]
Step: 4
The circumference of the circle is 10π.
Q5The diameter of the wheel of a truck is 100 cm. How many revolutions will it take to travel 700 cm.?

A. 7π
B. 6/π
C. 8/π
D. 7/π

Step: 1
Circumference of the wheel = πd
Step: 2
π × 100
[Substitute d = 100.]
Step: 3
100π cm.

Step: 4
The distance covered by the wheel in one revolution = Circumference of the circle
Step: 5
Number of revolutions of the wheel while travelling 700 cm.
700/100π = 7/π

Q6The circumference of two concentric circles is 160 m. and 132 m. What is the difference between their radii?
A. 14/π m
B. 14π m
C. π/14 m
D. 66/π m

Step: 1
Let r1 and r2 be the radii of outer and inner circles.
Step: 2
Circumference of the outer circle, 2πr1 = 160 m.
Step: 3
r1 = 80/π
[Divide each side by 2π.]
Step: 4
Circumference of the inner circle, 2πr2 = 132 m.
Step: 5
r2 = 66/π
[Divide each side by 2π.]
Step: 6
The difference between their radii = 80/π - 66/π
= 14/π m.

Correct Answer is :   14/π m
Q7If the diameter of a circle is increased by 80%, by what percent will its circumference increase?

A. 85%
B. 90%
C. 80%
D. 70%

Step: 1
Let d be the diameter of the circle.
Step: 2
The circumference of the circle = πd.
Step: 3
The diameter of a circle is increased by 80%.
Step: 4
The new diameter of the circle = (1 + 0.8) × d = 1.8d
Step: 5
The new circumference of the circle = π × 1.8d = 1.8 π d
Step: 6
The circumference of the circle is increased by 80%.
Q8If the radius of the circle is decreased by 30%, by what percent will its circumference decrease?

A. 30%
B. 60%
C. 55%
D. 65%

Step: 1
Let r be the radius of the circle.
Step: 2
The radius of a circle is decreased by 30%.
Step: 3
The new radius of the circle = (1 - 0.3) × r = 0.7r
Step: 4
Circumference of the circle = 2πr
Step: 5
The new circumference of the circle = 2 × π × 0.7r
Step: 6
= 0.7 × 2πr

Step: 7
= (1 - 0.3) × 2πr

Step: 8
So, the circumference of the circle is decreased by 30%.
Q9The diameter of a basketball hoop is 25 cm. What is its circumference? [Use π = 3.14.]

A. 74.50 cm
B. 68.50 cm
C. 78.50 cm
D. 88.50 cm

Step: 1
The circumference of a circle = π × diameter
Step: 2
= 3.14 × 25
[Substitute π = 3.14 and diameter = 25 cm.]
Step: 3
= 78.50 cm
Step: 4
The circumference of the basketball hoop is 78.50 cm.
Correct Answer is :   78.50 cm
Q10Estimate the diameter of a circle, if the circumference of the circle is 2.7 cm.

A. 1.1 cm
B. 1.0 cm
C. 0.8 cm
D. 0.9 cm

Step: 1
Circumference of a circle with diameter d = πd
[Formula.]
Step: 2
Circumference of the circle = 2.7cm.
Step: 3
From Steps(1) and (2), πd = 2.7
Step: 4
3 × d = 2.7
[Substitute π = 3.]
Step: 5
3d = 2.7
Step: 6
3d3 = 2.73
[Divide each side by 3.]
Step: 7
d = 0.9
[Simplify.]
Step: 8
The diameter of the circle is 0.9cm.
Correct Answer is :   0.9 cm
Q11John is walking along a circular flower garden. Which of the following measurements will help him find the distance covered?

A. volume
B. length
C. area
D. circumference

Step: 1
The shape of the garden is circle.
Step: 2
Therefore, the distance covered by John = the circumference of the circle.