Let's solve each of these
circle word problems step by step. We'll use the formula for the
circumference of a circle:
$$
C = \pi \times d \quad \text{or} \quad C = 2\pi r
$$
where:
- $ C $ is the circumference,
- $ d $ is the diameter,
- $ r $ is the radius,
- $ \pi \approx 3.14 $
---
Question 1:
> An architect is making a plan for a new circular playground. If the picture below is the playground, how much fencing needs to go up to keep the kids in the circle? Use 3.14 for π.
The diagram shows a circle with a
diameter of 64 meters.
We need the
circumference (since fencing goes around the edge).
$$
C = \pi \times d = 3.14 \times 64 = 200.96 \, \text{m}
$$
Rounded to the nearest whole number:
201 m
✔ Answer: C) 201 m
---
Question 2:
> The first Ferris wheel was built in 1893 in Chicago. Its diameter was 250 feet. How many feet did the Ferris wheel rotate with one complete turn?
One complete turn means the distance traveled is the
circumference.
$$
C = \pi \times d = 3.14 \times 250 = 785 \, \text{ft}
$$
✔ Answer: D) 785 ft
---
Question 3:
> The circumference of a circle is 36.31 meters. What is the approximate length of the radius? Use 3.14 for π.
Use the formula:
$$
C = 2\pi r \Rightarrow r = \frac{C}{2\pi}
$$
$$
r = \frac{36.31}{2 \times 3.14} = \frac{36.31}{6.28} \approx 5.78 \, \text{m}
$$
Approximately
6 meters
✔ Answer: D) 6 m
---
Question 4:
> The circumference of a circle is 18.41 feet. What is the approximate length of the radius? Use 3.14 for π.
Again:
$$
r = \frac{C}{2\pi} = \frac{18.41}{2 \times 3.14} = \frac{18.41}{6.28} \approx 2.93 \, \text{ft}
$$
Approximately
3 feet
✔ Answer: C) 3 ft
---
Question 5:
> A bicycle trail in the shape of a circle has a diameter of 3 miles. Kiersty biked around the trail 4 times. About how far did Kiersty bike? Use 3.14 for π.
First, find the
circumference of one loop:
$$
C = \pi \times d = 3.14 \times 3 = 9.42 \, \text{miles}
$$
She biked 4 times:
$$
4 \times 9.42 = 37.68 \, \text{miles}
$$
Now, look at the options:
- A) 40 miles
- B) 33 miles
37.68 is closer to
40 than to 33.
✔ Answer: A) 40 miles
---
✔ Final Answers:
1.
C) 201 m
2.
D) 785 ft
3.
D) 6 m
4.
C) 3 ft
5.
A) 40 miles
Let me know if you'd like explanations for the remaining questions too!
Parent Tip: Review the logic above to help your child master the concept of word problems for 7th grade math worksheet.
