Area of Circles

Show your work for each problem.

1.
What is the formula for the area of a circle?
1. a)
2. b)
3. c)
4. d)
Answer:
The area of a circle is where is the radius. is the circumference formula.
2.
A circle has a radius of 3 cm. What is its area? (Use and round to one decimal place)
Answer: 28.3
cm²
3.
If the radius of a circle is 5, what is ?
1. a)5
2. b)15
3. c)10
4. d)25
Answer: 25
. This is the first step in calculating circle area.
4.
A circle has a diameter of 10 cm. What is its radius?
Answer: 5
Radius cm
5.
Calculate the area of a circle with radius 4 cm. (Use )
Answer: 50.24
1. What formula do we use for circle area? πr²
2. What is when ? 16
3. What is ? 50.24
6.
A circle has a diameter of 14 cm. What is its area? (Use )
1. a)43.96 cm²
2. b)307.72 cm²
3. c)153.86 cm²
4. d)615.44 cm²
Answer: 153.86 cm²
Radius cm. Area cm²
7.
A circular garden has a radius of 6 meters. How many square meters of soil do you need to cover it? (Use )
Answer: 113.04
m²
8.
A pizza has a diameter of 30 cm. Calculate its area. (Use )
Answer: 706.5
1. What is the radius if the diameter is 30 cm? 15
2. What is ? 225
3. What is the area? () 706.5
9.
If you double the radius of a circle, what happens to the area?
1. a)It becomes 4 times larger
2. b)It stays the same
3. c)It becomes 8 times larger
4. d)It doubles
Answer: It becomes 4 times larger
If radius doubles: new area = = 4 times the original area.
10.
A circular tablecloth needs to cover a table with diameter 1.2 m. What area of fabric is needed? (Use )
Answer: 1.13
1. What is the radius in meters? 0.6
2. What is ? 0.36
3. What is the area? () 1.13
11.
Express the area of a circle with radius 8 cm in terms of π (as a multiple of π).
Answer: 64
cm². The coefficient of π is 64.
12.
A circular patio costs 45 euros per square meter to pave. If the radius is 4 m, what is the total cost? (Use )
Answer: 2260.8
1. What is the area of the patio? () 50.24
2. What is the cost per square meter? 45
3. What is the total cost? (Area × Cost per m²) 2260.8
13.
Circle A has radius 3 cm and Circle B has radius 6 cm. How many times larger is the area of Circle B compared to Circle A?
1. a)2 times
2. b)6 times
3. c)9 times
4. d)4 times
Answer: 4 times
Radius B = 2 × Radius A. Area ratio = . Circle B's area is 4 times Circle A's area.
14.
A circular pool has an area of 314 m². What is its radius? (Use )
Answer: 10
. Therefore m.
15.
A 35 cm diameter pizza costs 18 euros and a 25 cm diameter pizza costs 10 euros. Which pizza gives more area per euro?
Answer: 35 cm pizza
1. What is the radius of the 35 cm pizza? 17.5
2. What is the area of the 35 cm pizza? (Use π ≈ 3.14) 961.625
3. What is the area per euro for the 35 cm pizza? 53.4
4. What is the area per euro for the 25 cm pizza? (Area = 490.625) 49.1
5. Which pizza has more area per euro? 35 cm pizza
16.
A circular lawn sprinkler covers an area of 78.5 m². What is the maximum distance water reaches from the sprinkler? (Use )
Answer: 5
, so m. Water reaches 5 meters from the sprinkler.