Area of Circles Word Problems

Show your work for each problem.

1.
A circular flower bed has a radius of 3 meters. What is its area?
1. a) m² (≈ 9.4 m²)
2. b) m² (≈ 28.3 m²)
3. c) m² (≈ 37.7 m²)
4. d) m² (≈ 18.8 m²)
Answer: m² (≈ 28.3 m²)
square meters.
2.
A pizza has a diameter of 30 cm. What is the radius?
Answer: 15
Radius = diameter ÷ 2 = 30 ÷ 2 = 15 cm.
3.
Which formula gives the area of a circle?
1. a)
2. b)
3. c)
4. d)
Answer:
Area = (pi times radius squared). is the circumference, not area.
4.
A circular table has a radius of 2 feet. What is its area? Use and give your answer as a decimal.
Answer: 12.56
square feet.
5.
A circular pool has a diameter of 10 meters. What is its area? Use .
Answer: 78.5
1. What is the radius of the pool? 5
2. What is r² (radius squared)? 25
3. What is the area? (π × r²) 78.5
6.
A 14-inch pizza has approximately how much more area than a 10-inch pizza?
1. a)About 150 sq in more
2. b)About 4 sq in more
3. c)About 40 sq in more
4. d)About 75 sq in more
Answer: About 75 sq in more
14-inch: sq in. 10-inch: sq in. Difference ≈ 75 sq in.
7.
A circular rug has an area of 50.24 square feet. What is its radius? Use .
Answer: 4
, so feet.
8.
A circular pool cover costs 15 dollars per square meter. If the pool has a radius of 4 meters, how much will the cover cost? Use .
Answer: 753.6
1. What is r² (4 squared)? 16
2. What is the area of the pool? 50.24
3. What is the total cost? 753.6
9.
If you double the radius of a circle, what happens to its area?
1. a)The area quadruples (4×)
2. b)The area doubles (2×)
3. c)The area triples (3×)
4. d)The area stays the same
Answer: The area quadruples (4×)
If r → 2r, then . The area becomes 4 times larger!
10.
Grass seed covers 8 square meters per bag. A circular lawn has a diameter of 6 meters. How many bags do you need?
Answer: 4
1. What is the radius of the lawn? 3
2. What is the area of the lawn? (Use π ≈ 3.14) 28.26
3. How many bags needed (round up)? 4
11.
Two pizzas: a 30 cm for 12 euros, or a 40 cm for 20 euros. Which gives more pizza per euro?
Answer: 40
1. What is the area of the 30 cm pizza? (radius = 15) 706.5
2. What is the area per euro for the 30 cm? 58.875
3. What is the area of the 40 cm pizza? (radius = 20) 1256
4. What is the area per euro for the 40 cm? 62.8
5. Which pizza is better value? (30 or 40) 40
12.
A circular garden has an area of 78.5 square meters. What is its diameter? Use .
Answer: 10
, so m. Diameter = m.
13.
A sprinkler waters a circular area. If the sprinkler's reach increases from 5m to 7m, by how much does the watered area increase?
1. a)About 153.9 m²
2. b)About 37.7 m²
3. c)About 12.6 m²
4. d)About 75.4 m²
Answer: About 75.4 m²
At 5m: m². At 7m: m². Increase = 153.9 - 78.5 = 75.4 m².
14.
Paint costs 25 dollars per can and covers 10 m². A circular ceiling has a radius of 3 meters. How much will it cost to paint it?
Answer: 75
1. What is the ceiling area? (Use π ≈ 3.14) 28.26
2. How many cans needed? (Round up) 3
3. What is the total cost? 75
15.
A circular trampoline has a jumping area of 12.56 m². If you want one with 4 times the area, what radius do you need?
Answer: 4
Original: , so m. For 4× area, radius = m.