# Solutions: Circumference & Area of Circles

#### Circumference of Circles

Exercise |
Problem |
Solution |

1 | The diameter of a nickel is 2 cm. What is the circumference? | d = 2 cm; C = 3.14 (2 cm); C = 6.28 cm |

2 | The circumference of a bicycle wheel is 50.24 in. What is the diameter? | C = 50.24 in; d = 50.24 in ÷ 3.14; C = 16 in |

3 | The radius of a circular rug is 4 ft. What is the circumference? | r = 4 ft; d = 8 ft; C = 3.14 (8 ft); C = 25.12 ft |

4 | The circumference of a compact disc is 28.26 centimeters. What is the radius? | C = 28.26 cm; d = 28.26 cm ÷ 3.14; d= 9 cm; r = 4.5 cm |

5 | The diameter of your bicycle wheel is 25 in. How far will you move in one turn of your wheel? | d = 25 in; C = 25 in (3.14); C = 78.5 in |

#### Area of Circles

Exercise |
Problem |
Solution |

1 | The radius of a circle is 9 cm. What is the area? | r = 9 cm; A = 3.14 (9 cm) (9 cm); A = 254.34 cm^{2} |

2 | The diameter of a circle is 12 in. What is the area? | d = 12 in; r = 6 in; A = 3.14 (6 in) (6 in); A = 113.04 in^{2} |

3 | The radius of a circular rug is 4 feet. What is the area? | r = 4 ft; A = 3.14 (4 ft) (4 ft); A = 50.24 ft^{2} |

4 | The area of a coin is 3.14 square centimeters. What is the radius? | A = 3.14 cm^{2}; (r)(r) = 3.14 cm^{2} ÷ 3.14;(r)(r) = 1 cm ^{2}; r = 1 cm |

5 | The diameter of a bicycle wheel is 20 in. What is the area of the wheel? | d = 20 in; r = 10 in; A = 3.14 (10 in)(10 in); A= 314 in ^{2} |

#### Practice Exercises

Exercise |
Problem |
Solution |

1 | If the diameter of a circle is 142.8 mm, then what is the radius? | d = 142.8 mm; r = 142.8 ÷ 2; r = 71.4 mm |

2 | If the radius of a circle is 15.3 cm, then what is the diameter? | r = 15.3 cm; d = 15.3 cm · 2; d = 30.6 cm |

3 | Find the circumference of a circle with a diameter of 11 mm. | d = 11 mm; C = (11 mm)(3.14); C = 34.54 mm |

4 | Find the circumference of a circle with a diameter of 7.5 in. | d = 7.5 in; C = (3.14)(7.5 in); C = 23.55 in |

5 | Find the diameter of a circle with a circumference of 21.98 m. | C = 21.98 m; d = 21.98 m ÷ 3.14; d = 7 m (or 7.0 m) |

6 | Find the area of a circle with a radius of 4 in. | A = (4 in)(4 in)(3.14); A = (16 in^{2})(3.14);A = 50.24 in ^{2} |

7 | Find the area of a circle with a radius of 3.5 cm. (Do not round. Enter your answer to three decimal places.) | r = 3.5 cm; A = (3.5 cm)(3.5 cm)(3.14); A = (12.25 cm ^{2})(3.14); A = 38.465 cm^{2} |

8 | Find the radius of a circle with an area of 200.96 square feet. | A = 200.96 ft^{2}; 200.96 ft^{2} ÷ 3.14 = r^{2};64 ft ^{2} = r^{2}; r = 8 ft. |

9 | If the radius of a circle is 1.5 in, then what is the circumference? | r = 1.5 in; d = 2 · 1.5 in; d = 3.0 in;C = (3.14)(3 in) = 9.42 in. |

10 | If the diameter of a circle is 9 cm, then what is the area? (Do not round. Enter your answer to three decimal places.) | d = 9 cm; r = 9 cm ÷ 2; r = 4.5 cm;A = (4.5 cm)(4.5 cm)(3.14); A = (20.25 cm ^{2})(3.14);A = 63.585 cm ^{2} |

### Challenge Exercises

Exercise |
Problem |
Solution |

1 | A dinner plate has a radius of 6 cm. What is the area? | r = 6 cm; A = 3.14(6 cm)(6 cm); A = 113.04 cm ^{2} |

2 | The distance around the wheel of a truck is 9.42 ft. What is the diameter of the wheel? | C = 9.42 ft; d = 9.42 ÷ 3.14 = 3 ft |

3 | A lawn sprinkler sprays water 5 ft in every direction as it rotates. What is the area of the sprinkled lawn? | r = 5 ft; A = 3.14(5 ft)(5 ft); A = 78.5 ft^{2} |

4 | What is the circumference of a 12-inch pizza? | d = 12 in; C = 3.14(12 in); C = 37.68 in |

5 | A dog is tied to a wooden stake in a yard. His leash is 3 m long, and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in? | r = 3 m; A = 3.14(3 m)(3 m); A = 28.26 m^{2} |

6 | The distance around a carousel is 21.98 yd. What is the radius? | C = 21.98 yd; d = 21.98 yd ÷ 3.14;d = 7 yd; r = 3.5 yd |

7 | A storm is expected to hit 7 mi in every direction from a small town. What is the area that the storm will affect? | r = 7 mi; A = 3.14(7 mi)(7 mi); A = 153.86 mi^{2} |

8 | An asteroid hit the earth and created a huge round crater. Scientists measured the distance around the crater as 78.5 mi. What is the diameter of the crater? | C = 78.5 mi; d = 78.5 mi ÷ 3.14; d = 25 mi |

9 | A semi-circle shaped rug has a diameter of 2 ft. What is the area of the rug? | d = 2 ft; r = 1 ft; Area of circle = 3.14(1 ft (1 ft); Area of Circle = 3.14 ft ^{2};Area of semi-circle = 3.14 ft ^{2} ÷ 2;Area of semi-circle = 1.57 ft ^{2} |

10 | A spinner has 6 sectors, half of which are red and half of which are black. If the radius of the spinner is 3 in, what is the area of the red sectors? | r = 3 in; Area of spinner = 3.14(3 in)(3 in) Area of Spinner = 28.26 in ^{2};Area of red sectors = 28.26 in ^{2} ÷ 2;Area of red sectors = 14.13 in ^{2} |