A circle has area 4π cm². Find its diameter.
Show reasoning / computation: __________________________________________
CCSS 7.G.B.4 · area, circumference, radius & diameter
Circle Area and Circumference Worksheet Generator
Practice the relationship among radius, diameter, circumference, and area. Use exact π mode when symbolic answers are preferred or switch to π ≈ 3.14 for decimal computation practice.
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Circle Area & Circumference
Diagrams are part of the problem data, not decorative assets. Student pages keep solution-specific marks hidden; reveal answers or use the separate PDF key to check work.
Problem 1
Problem 2
A circle has radius 9 cm. Find both circumference and area using π exactly.
Show reasoning / computation: __________________________________________
Problem 3
A circle has area 16π cm². Find its diameter.
Show reasoning / computation: __________________________________________
Problem 4
A circle has circumference 16π cm. Find its radius.
Show reasoning / computation: __________________________________________
Problem 5
A circle has radius 5 cm. Find its area using π exactly.
Show reasoning / computation: __________________________________________
Problem 6
A circle has area 64π cm². Find its diameter.
Show reasoning / computation: __________________________________________
Problem 7
A circle has radius 4 cm. Find both circumference and area using π exactly.
Show reasoning / computation: __________________________________________
Problem 8
A circle has radius 6 cm. Find its area using π exactly.
Show reasoning / computation: __________________________________________
Finding the area and circumference of a circle
The circumference is the distance around a circle, C = 2πr or C = πd. The area is the space inside, A = πr², and the radius is squared before multiplying by π. The radius is half the diameter, so check which one the problem gives. Use 3.14 for π unless the problem says otherwise, and give the answer in the right units.
Worked examples
- Radius 5 cm: C = 2 × π × 5 = 10π ≈ 31.4 cm, and A = π × 5² = 25π ≈ 78.5 cm².
- Diameter 12 m: the radius is 6 m, so A = π × 6² = 36π ≈ 113.04 m².
- Diameter 6 in: C = π × 6 = 6π ≈ 18.84 in.
- Why the formulas connect: cut a circle into many narrow sectors and alternate them point-up and point-down. They approach a parallelogram with height r and base C ÷ 2, so its area approaches (C ÷ 2) × r = (2πr ÷ 2) × r = πr².
- A circular garden has radius 3 m. It needs about 18.84 m of fencing because C = 2 × 3.14 × 3, and its area is about 28.26 m² because A = 3.14 × 3².
Common slips
- Using the diameter in the area formula. For a diameter of 12, use r = 6, not 12.
- Multiplying the radius by 2 instead of squaring it. 5² is 25, not 10.
- Mixing the units: area is in square units, such as cm², and circumference is in plain units, such as cm.
How to use this worksheet
Ask students to write the radius first and then the formula they chose. The answer key gives the answers in terms of π and as decimals, so both forms can be compared.
Common Core connection
- 7.G.B.4 · Use formulas for circles to solve problems involving circumference and area.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Diameter is twice the radius before any circle formula is applied. Using the diameter where the radius belongs, or squaring the diameter for area, is the most common error.
Note 2
Circumference uses a linear measure; area uses square units.
Note 3
Example: radius 5 gives circumference 2 times pi times 5, or 10 pi (about 31.4), and area pi times 5 squared, or 25 pi (about 78.5).
Note 4
Do not round early. When π ≈ 3.14 is selected, the generator computes from the exact integer radius first.
Continue the 7.G progression
Move to another Grade 7 geometry skill
Quick answers
Can I choose exact π answers?
Yes. The generator has an exact π mode and a π ≈ 3.14 mode.
Do challenge sets include reverse problems?
Yes. Standard and challenge sets can ask for a missing radius from circumference or a missing diameter from area.
Which standard does this practice?
CCSS 7.G.B.4: know and use the formulas for the area and circumference of a circle and solve problems, including the informal derivation of the relationship between circumference and area.