Parts of a Circle and Circumference

Show your work for each problem.

1.
What is the relationship between diameter and radius?
1. a)
2. b)
3. c)
4. d)
Answer:
The diameter is always twice the radius because it spans from one edge through the center to the opposite edge, which is two radii.
2.
Which formula correctly calculates the circumference using the radius?
1. a)
2. b)
3. c)
4. d)
Answer:
is correct. Note that gives area, not circumference, and is missing the factor of 2.
3.
A circle has a radius of cm. What is its diameter in cm?
Answer: 10
cm. The diameter is always twice the radius.
4.
A circle has a diameter of cm. What is its radius in cm?
Answer: 7
cm. The radius is always half the diameter.
5.
Find the circumference of a circle with radius cm. Use .
Answer: 43.96
1. Which formula do you use for circumference with radius? C = 2 * pi * r
2. Substitute : What is ? 14
3. Now multiply by : What is ? 43.96
6.
Find the circumference of a circle with diameter m. Use .
Answer: 31.4
1. Which formula do you use for circumference with diameter? C = pi * d
2. Substitute : What is ? 31.4
7.
A circular pond has a circumference of m. Using , what is its diameter?
1. a) m
2. b) m
3. c) m
4. d) m
Answer: m
m. The other answers: 10 m is the radius, 31.4 m is half the circumference, and 40 m is diameter doubled.
8.
A wheel has a circumference of cm. What is its radius in cm? Use .
Answer: 30
cm.
9.
A circular track has a circumference of m. Find its radius. Use and round to one decimal place.
Answer: 63.7
1. From , what is the formula for ? r = C / (2 * pi)
2. What is ? 6.28
3. What is ? 63.7
10.
A pizza has a diameter of cm. How far does a pizza cutter travel if it goes around the entire edge? Use .
Answer: 94.2
1. The distance around the pizza is called the... circumference
2. Which formula uses diameter? pi * d
3. What is ? 94.2
11.
If you double the radius of a circle, what happens to its circumference?
1. a)It stays the same
2. b)It doubles
3. c)It triples
4. d)It quadruples
Answer: It doubles
Since , if doubles, doubles too. Quadrupling would happen with area (), not circumference.
12.
A bicycle wheel makes complete rotations to travel km. What is the diameter of the wheel in cm? Use and round to the nearest whole number.
Answer: 64
1 km = 100,000 cm. Circumference = cm. Then cm.
13.
A circular fountain has a fence around it. The fence is meters from the edge of the fountain. If the fountain's diameter is m, how long is the fence? Use .
Answer: 43.96
1. The fountain has diameter m, so its radius is... 4
2. The fence is m further out. What is the fence's radius? 7
3. The fence forms a larger circle. What is its diameter? 14
4. What is the circumference of the fence? 43.96
14.
Two circles have circumferences of cm and cm. What is the difference between their radii in cm? Use .
Answer: 5
cm. cm. Difference = cm.
15.
A semicircle has a diameter of cm. What is the total perimeter (curved part + straight edge)? Use .
1. a) cm
2. b) cm
3. c) cm
4. d) cm
Answer: cm
Curved part = cm. Total = cm. The other answers: 31.4 is just the curved part, 62.8 is full circumference, 41.4 uses radius instead of diameter.