The distance around the outside of a circle is called the circumference. The distance from the center of the circle to any point on the circle is called the radius. The number of square units needed to cover the inside of a circle is called the area. The distance across a circle through its center is called the diameter. Write the following formulas: 5. Circumference when the radius is given: C = 2Ï€r 6. Circumference when the diameter is given: C = Ï€d 7. Area of a circle: A = Ï€r^2 Find the circumference of each circle; Round to the nearest tenth. (Show your work and don’t forget to label your answer): 8. Radius = 8 cm: C = 2Ï€(8) = 16Ï€ ≈ 50.3 cm 9. Diameter = 17 m: C = Ï€(17) ≈ 53.4 m Find the area of each circle: Round to the nearest tenth: (Show your work and don’t forget to label your answer): 10. Radius = 3 in: A = Ï€(3)^2 ≈ 28.3 in^2 11. Diameter = 9 ft: A = Ï€(9/2)^2 ≈ 63.6 ft^2
The Correct Answer and Explanation is:
5. Circumference when the radius is given
Formula: C = 2πr
6. Circumference when the diameter is given
Formula: C = πd
7. Area of a circle
Formula: A = πr²
8. Radius = 8 cm
C = 2πr
= 2 × π × 8
= 16π ≈ 16 × 3.1416 ≈ 50.3 cm
Answer: 50.3 cm
9. Diameter = 17 m
C = πd
= π × 17 ≈ 3.1416 × 17 ≈ 53.4 m
Answer: 53.4 m
10. Radius = 3 in
A = πr²
= π × 3² = π × 9 ≈ 3.1416 × 9 ≈ 28.3 in²
Answer: 28.3 in²
11. Diameter = 9 ft
Radius = diameter ÷ 2 = 9 ÷ 2 = 4.5 ft
A = πr²
= π × (4.5)² = π × 20.25 ≈ 3.1416 × 20.25 ≈ 63.6 ft²
Answer: 63.6 ft²
Explanation
Understanding the geometry of a circle is essential in many areas of math and real life. Four key terms related to a circle include the radius, diameter, circumference, and area. The radius is the distance from the center to any point on the circle. The diameter is twice the length of the radius, stretching from one point on the circle to another, passing through the center. The circumference is the perimeter or distance around the circle. The area measures the surface inside the circle in square units.
To find the circumference, we use two formulas based on what is known:
- If the radius is given, use C = 2πr
- If the diameter is given, use C = πd
In both cases, π (pi) is approximately 3.1416. This constant represents the ratio of a circle’s circumference to its diameter.
To calculate the area, we use the formula A = πr², where r is the radius. This formula comes from the concept of how many square units fill the inside of the circle.
When doing calculations, it is important to follow the order of operations, squaring the radius before multiplying by π. Answers are usually rounded to the nearest tenth unless instructed otherwise, and units must be included, such as cm, m, in², or ft², depending on the measurement used.
These basic circle formulas help solve many problems in geometry, engineering, and design
