Area of Annulus (Ring)

Show your work for each problem.

1.
What is an annulus?
1. a)A circle with a tangent line
2. b)A full circle
3. c)A semicircle
4. d)A ring-shaped region between two concentric circles
Answer: A ring-shaped region between two concentric circles
An annulus is the region between two concentric circles (circles sharing the same center but with different radii). It looks like a ring or washer.
2.
Which formula calculates the area of an annulus with outer radius and inner radius ?
1. a)
2. b)
3. c)
4. d)
Answer:
The annulus area is , which factors to . We subtract the areas, not the radii.
3.
An annulus has outer radius cm and inner radius cm. Calculate .
Answer: 12
. The area would be cm.
4.
Find the area of an annulus with cm and cm. Give your answer as a multiple of (just the number).
Answer: 9
cm.
5.
Calculate the area of an annulus with outer radius 6 cm and inner radius 2 cm.
Answer: 32pi
1. What is ? (outer radius squared) 36
2. What is ? (inner radius squared) 4
3. What is ? 32
4. What is the area as a multiple of ? 32
6.
A pipe has outer diameter 8 cm and inner diameter 6 cm. What is the cross-sectional area of the pipe material?
1. a) cm
2. b) cm
3. c) cm
4. d) cm
Answer: cm
Radii: cm, cm. Area cm.
7.
A circular garden has radius 5 m. A 2 m wide path surrounds it. What is the area of the path? Give answer as a multiple of .
Answer: 24
m, m. Area m.
8.
A washer has outer radius 15 mm and inner radius 8 mm. Calculate the area in mm. Round to the nearest whole number.
Answer: 506
mm.
9.
A pipe has outer diameter 12 cm and wall thickness 2 cm. Find the cross-sectional area of the pipe material.
Answer: 20pi
1. What is the outer radius ? 6
2. The wall is 2 cm thick. What is the inner radius ? 4
3. Calculate : 20
4. What is the area as a multiple of ? 20
10.
A dartboard ring has inner radius 50 mm and outer radius 70 mm. Find its area.
Answer: 2400pi
1. What is ? 4900
2. What is ? 2500
3. What is ? 2400
4. What is the area as a multiple of ? 2400
11.
If you double both radii of an annulus, by what factor does the area increase?
1. a)4 times
2. b)8 times
3. c)2 times
4. d) times
Answer: 4 times
Original: . After doubling: . The area quadruples!
12.
An annulus has area cm and outer radius 5 cm. What is the inner radius?
Answer: 2
, so , giving , thus cm.
13.
A CD has inner recording radius 23 mm and outer recording radius 58 mm. What is the recording area in mm? Round to the nearest integer.
Answer: 8906
mm.
14.
A circular fountain (radius 3 m) is surrounded by a 1.5 m wide walkway, which is bordered by a 0.5 m wide flower bed. Find the total area of walkway plus flower bed.
Answer: 16pi
1. What is the inner radius (fountain)? 3
2. What is the outer radius (fountain + walkway + flower bed)? 5
3. Calculate : 16
4. What is the total area as a multiple of ? 16
15.
Two annuli have the same area. The first has and . The second has . Find .
Answer: 0
1. Calculate the area of the first annulus (multiple of ): 64
2. For equal areas: . What is ? 0
3. What is ? 0