Resources/Circles: circumference and area
Grade 7•Printable worksheet + answer key•CC0 license

Circles: circumference and area

A printable lesson on pi, circumference, and area of circles.

Students learn to calculate circumference using C = πd and area using A = πr², with real-world applications.

Print-ready worksheet with answer key and quick teaching tips.

Grade 70 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free circles worksheet for grade 7 builds mastery of circumference and area formulas using pi (π ≈ 3.14).

Lesson plan snapshot

15-20 min
  • Warm-up (3 min): review what radius and diameter mean.
  • Model (5 min): solve the worked example together.
  • Guided practice (5 min): complete problems 1-4 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: calculator, pencil, compass (optional)

Learning targets

  • Understand pi as the ratio of circumference to diameter.
  • Calculate circumference using C = πd or C = 2πr.
  • Calculate area using A = πr².
  • Apply formulas to real-world problems.

Step-by-step approach

  1. 1Identify whether you're given radius or diameter.
  2. 2For circumference: use C = πd or C = 2πr.
  3. 3For area: use A = πr² (remember to square the radius first!).
  4. 4Use π ≈ 3.14 unless told to leave answer in terms of pi.
  5. 5Include units: linear for circumference, square for area.

Common mistakes

Mistake

Forgetting to square the radius for area.

Try instead

Write the formula first: A = π × r × r. Square radius before multiplying by pi.

Mistake

Confusing radius and diameter.

Try instead

Diameter is twice the radius. If given diameter, divide by 2 for radius.

Mistake

Using circumference formula for area.

Try instead

Think: circumference goes AROUND, area fills INSIDE. C uses 2r, A uses r².

Worked example

Guided
A circle has radius 5. Find the circumference and area.
r = 5
  1. Circumference: C = 2πr = 2 × 3.14 × 5 = 31.4
  2. Area: A = πr² = 3.14 × 5² = 3.14 × 25 = 78.5
Answer: Circumference = 31.4 units, Area = 78.5 square units

Related resources

Area & perimeter

Foundational area concepts with rectangles.

View resource

Geometry

Shape properties and geometry foundations.

View resource

Practice problems

10 problems • 15 min

Printable worksheet
  1. 1
    Circle A has radius 3. Circle B has radius 6. How many times larger is the area of Circle B compared to Circle A?
  2. 2
    Find the area of a circle with radius 4. Use π ≈ 3.14.
  3. 3
    Find the area of a semicircle with diameter 8. Use π ≈ 3.14.
  4. 4
    A circle has circumference 15.7. What is the diameter? Use π ≈ 3.14.
  5. 5
    A circle has circumference 18.84. What is the radius? Use π ≈ 3.14.
  6. 6
    Find the circumference of a circle with radius 4. Use π ≈ 3.14.
  7. 7
    Find the circumference of a circle with diameter 5. Use π ≈ 3.14.
  8. 8
    Find the area of a circle with radius 3. Use π ≈ 3.14.
  9. 9
    Find the area of a circle with diameter 14. Use π ≈ 3.14.
  10. 10
    A circle has circumference 25.12. What is the diameter? Use π ≈ 3.14.

Answer key

10 answers
  1. 11) 4
  2. 22) 50.24
  3. 33) 25.12
  4. 44) 5
  5. 55) 3
  6. 66) 25.12
  7. 77) 15.7
  8. 88) 28.26
  9. 99) 153.86
  10. 1010) 8

Teacher tips

  • THave students measure real circular objects with string to discover pi.
  • TEmphasize that area always involves squaring - it's measuring 2D space.
  • TUse the pizza analogy: circumference is crust, area is the whole pizza.

Parent tips

  • PAsk about circles you see: plates, wheels, clocks - what's the radius?
  • PPractice with different sized pizzas to compare areas.
  • PHelp your child remember: around = circumference, inside = area.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).