Question

a. choose the correct choice.

1. a circle has a circumference of 138.16 m. what is the diameter of the circle?

a) 22 m b) 44 m c) 88 m

1. an iron rod of length 10.38 ft is bent to form a circle. what is the radius of the circle?

a) 1.65 ft b) 3.3 ft c) 6.6 ft

1. a circular paddy field has a circumference of 89.18 in. find its diameter.

a) 56.8 in b) 28.4 in c) 28.4 in

1. the tip of the minute - hand travels 103.62 mm in one hour. find the length of the minute - hand.

a) 33 mm b) 16.5 mm c) 18.5 mm

1. the circumference of a circular plate is 49.67 cm. find the diameter of plate.

a) 7.91 cm b) 3.14 cm c) 15.82 cm
b. find the radius and diameter in each question.

s.no	circumference	radius	diameter
7.	77.24 ft
8.	157 in
9.	31.34 cm
10.	75.36 ft

Explanation:

Step1: Recall circle - formulas

The formula for the circumference of a circle is $C = \pi d=2\pi r$, where $C$ is the circumference, $d$ is the diameter and $r$ is the radius. We can use $d=\frac{C}{\pi}$ and $r = \frac{C}{2\pi}$ for calculations. Assume $\pi\approx3.14$.

Step2: Solve question 1

Given $C = 138.16$ m. Using $d=\frac{C}{\pi}$, we have $d=\frac{138.16}{3.14}=44$ m. So the answer is b).

Step3: Solve question 2

Given $C = 10.38$ ft. Using $r=\frac{C}{2\pi}$, we have $r=\frac{10.38}{2\times3.14}=\frac{10.38}{6.28}\approx1.65$ ft. So the answer is a).

Step4: Solve question 3

Given $C = 89.18$ in. Using $d=\frac{C}{\pi}$, we have $d=\frac{89.18}{3.14}=28.4$ in. So the answer is b) and c) (they are the same).

Step5: Solve question 4

The distance the tip of the minute - hand travels in one hour is the circumference of the circle it makes. Given $C = 103.62$ mm. Using $r=\frac{C}{2\pi}$, we have $r=\frac{103.62}{2\times3.14}=\frac{103.62}{6.28}=16.5$ mm. So the answer is b).

Step6: Solve question 5

Given $C = 49.67$ cm. Using $d=\frac{C}{\pi}$, we have $d=\frac{49.67}{3.14}=15.82$ cm. So the answer is c).

Step7: Solve question 6

Given $C = 39.94$ m. $r=\frac{C}{2\pi}=\frac{39.94}{2\times3.14}=\frac{39.94}{6.28}\approx6.36$ m, $d=\frac{C}{\pi}=\frac{39.94}{3.14}\approx12.72$ m.

Step8: Solve question 7

Given $C = 77.24$ ft. $r=\frac{C}{2\pi}=\frac{77.24}{2\times3.14}=\frac{77.24}{6.28}=12.3$ ft, $d=\frac{C}{\pi}=\frac{77.24}{3.14}=24.6$ ft.

Step9: Solve question 8

Given $C = 157$ in. $r=\frac{C}{2\pi}=\frac{157}{2\times3.14}=\frac{157}{6.28}=25$ in, $d=\frac{C}{\pi}=\frac{157}{3.14}=50$ in.

Step10: Solve question 9

Given $C = 31.34$ cm. $r=\frac{C}{2\pi}=\frac{31.34}{2\times3.14}=\frac{31.34}{6.28}\approx5$ cm, $d=\frac{C}{\pi}=\frac{31.34}{3.14}\approx10$ cm.

Step11: Solve question 10

Given $C = 75.36$ ft. $r=\frac{C}{2\pi}=\frac{75.36}{2\times3.14}=\frac{75.36}{6.28}=12$ ft, $d=\frac{C}{\pi}=\frac{75.36}{3.14}=24$ ft.

Answer:

1. b) 44 m
2. a) 1.65 ft
3. b) 28.4 in
4. b) 16.5 mm
5. c) 15.82 cm
6. Radius: approximately 6.36 m, Diameter: approximately 12.72 m
7. Radius: 12.3 ft, Diameter: 24.6 ft
8. Radius: 25 in, Diameter: 50 in
9. Radius: approximately 5 cm, Diameter: approximately 10 cm
10. Radius: 12 ft, Diameter: 24 ft