Circle worksheet: radius, diameter, circumference and area
Twelve problems in four levels: radius and diameter, circumference, area and working backward (finding the radius from the circumference or from the area). The figures always use the same key: the orange edge is the circumference to find and the shaded inside is the area, so students don't mix them up.
It includes real-world problems (how far a bike wheel goes, how many times more pizza you get with twice the diameter) and a box with the typical mistakes, like using the diameter instead of the radius.
What's included
- 2 student pages: 12 problems in 4 levels, with figures and a grid to work on.
- Answers at the bottom (printed upside down) and a box with the most common mistakes.
- 1 teacher page: answer key with π ≈ 3.14 and with the π key, common mistakes and an exit question.
Check your answers
The problems
7 cm given? unknownformula
Use π ≈ 3.14 (with the π key, the decimals may be a little different). What is on the edge is circumference; what is inside is area.
d = 2 · r │ C = π · d = 2 · π · r │ A = π · r²
orange edge: circumference to find shaded inside: area to findFigures not to scale.
●○○Level 1 · Radius and diameter
1
How long is the diameter?
2
How long is the radius?
3
A quarter has a diameter of about 2.4 cm. What is its radius?
●●○Level 2 · Circumference
4
Find the circumference of a circle with a diameter of 20 cm.
5
Find the circumference.
6
A bike wheel has a diameter of 66 cm. How far does it go in one turn? And in 100 turns, in meters?
●●○Level 3 · Area
7
Find the area.
8
A pizza has a diameter of 30 cm. What is its area?
9
How many times more pizza does the large one have than the small one? Find both areas.
●●●Level 4 · Working backward
10
The circumference is 50 cm. How long is the diameter? And the radius?
11
A circle has an area of 100 cm². How long is its radius?
12
A circular garden has an area of 314 m². How many meters of fence do you need to go around it?
Got a different number? Check: #4 → 125.6: you used 2 · π with the diameter · #7 → 31.4: you did r · 2 instead of r · r; 246.49: you squared (π · r) · #8 → 2826: you used the diameter in π · r² · #9 → 2: when the diameter doubles, the area is multiplied by 4 · #10 → 157: you multiplied by π instead of dividing · #11 → 31.85: you forgot the square root.
Answers: 1) 8 cm · 2) 7.5 cm · 3) 1.2 cm · 4) 62.8 cm · 5) 31.4 cm · 6) 207.24 cm; about 207 m · 7) 78.5 cm² · 8) 706.5 cm² · 9) 176.63 and 706.5 cm²: 4 times · 10) d ≈ 15.92 cm; r ≈ 7.96 cm · 11) r ≈ 5.64 cm · 12) r = 10 m; C = 62.8 m
For the teacher: answer key and common mistakes
Answer key (π ≈ 3.14; in parentheses, with the π key)
- d = 2 · 4 = 8 cm
- r = 15 ÷ 2 = 7.5 cm
- r = 2.4 ÷ 2 = 1.2 cm
- C = 3.14 · 20 = 62.8 cm (62.83)
- C = 2 · 3.14 · 5 = 31.4 cm (31.42)
- C = 3.14 · 66 = 207.24 cm (207.35); 100 turns ≈ 20,724 cm ≈ 207 m
- A = 3.14 · 5² = 78.5 cm² (78.54)
- r = 15 cm; A = 3.14 · 225 = 706.5 cm² (706.86)
- small: r = 7.5 → 176.63 cm²; large: 706.5 cm² → 4 times (the diameter doubles, the area quadruples)
- d = 50 ÷ 3.14 ≈ 15.92 cm; r ≈ 7.96 cm
- r = √(100 ÷ 3.14) ≈ √31.85 ≈ 5.64 cm
- r² = 314 ÷ 3.14 = 100 → r = 10 m; C = 2 · 3.14 · 10 = 62.8 m
Mistakes to watch for
- Using the diameter as if it were the radius (the most common one).
- Calculating r² as r · 2 or as (π · r)².
- Forgetting the square root when working backward from the area.