The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Two formulas to memorize
- 1Circumference: C = πd (or C = 2πr).
- 2Area: A = πr² (radius times itself, then times π).
A circle has radius 5 cm. Find its circumference and area (use π ≈ 3.14).
- 1Circumference: C = 2πr = 2 × 3.14 × 5 = 31.4 cm.
- 2Area: A = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm².
Why this matters
Use π with the radius and diameter to measure circles.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Two formulas to memorize
- Circumference: C = πd (or C = 2πr).
- Area: A = πr² (radius times itself, then times π).
Video walkthroughs
Circles, Circumference and Area
Use π with radius and diameter to find both measures.
Watch on YouTube
Circumference of a Circle
Relate radius, area, and circumference using pi.
Watch on YouTube
Composite Area Related to Circles
Find shaded area by combining circles and other shapes.
Watch on YouTube
Cylinder Volume & Surface Area
Apply circle area and circumference formulas to cylinders.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfA circle has radius 7 cm. Find the circumference using C = 2πr and π ≈ 3.14.
Step-by-step solution
- 1C = 2 × 3.14 × 7 = 43.96 cm.
Exercise 2
Try it yourselfA circle has diameter 12 m. Find the circumference (π ≈ 3.14).
Step-by-step solution
- 1C = πd = 3.14 × 12 = 37.68 m.
Exercise 3
Try it yourselfA circle has radius 4 in. Find the area (π ≈ 3.14).
Step-by-step solution
- 1A = πr² = 3.14 × 4² = 3.14 × 16 = 50.24 in².
Exercise 4
Try it yourselfA circular pizza has diameter 14 in. Find the area (π ≈ 22/7).
Step-by-step solution
- 1Radius r = 7 in.
- 2A = πr² = (22/7) × 49 = 22 × 7 = 154 in².
Exercise 5
Try it yourselfA semicircular window has diameter 10 ft. Find the perimeter of the window (straight diameter + curved half). Use π ≈ 3.14.
Step-by-step solution
- 1Radius = 5 ft.
- 2Half circumference = (1/2)(2πr) = πr = 3.14 × 5 = 15.7 ft.
- 3Add diameter 10 ft: 15.7 + 10 = 25.7 ft.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Circumference & Area of Circles
Question 1 of 4
A circle has a diameter of 10 m. What is its circumference? (π ≈ 3.14)