7th grade · Math · Unit 5 of 17
Circles
Circumference, area and π
What your child practices
Using radius, diameter and π (about 3.14) to find the distance around a circle and the area inside it, including real objects like wheels and pizzas.
Alaska content standards learning standard: 7.G.4 · circumference and area of circles
How we explain it
Children can open this short lesson before they practice.
- The radius goes from the center to the edge. The diameter goes all the way across: d = 2r.
- Circumference (the distance around) is C = π × d.
- Area is A = π × r × r. Use π ≈ 3.14.
Example: A circle has diameter 10 cm. What is its circumference? C = π × d. C ≈ 3.14 × 10 = 31.4. Answer: About 31.4 cm
Circles in Alaska
In the Alaska content standards, this is unit 5 of 17 in 7th grade Math, after Two-Step Equations and before Volume.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Alaska Department of Education and Early Development
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A bike wheel has a diameter of 50 cm. How far does the bike roll in one full turn of the wheel? Use 3.14 for π and round to one decimal place.
🚲d = 50 cmanswer boxcm
157.0 cm
Hint: One turn rolls one circumference: 3.14 × 50 = 157 cm.
Question 2
A circle has a radius of 7 m. What is its circumference? Use 3.14 for π and round to one decimal place.
⭕r = 7 manswer boxm
44.0 m
Hint: C = 2 × π × r ≈ 2 × 3.14 × 7 = 43.96. Rounded: 44.0 m. (Or double the radius to get d = 14, then 3.14 × d.)
Question 3
A circle has a radius of 12 cm. What is its diameter?
⭕r = 12 cm- 6 cm
- 24 cm
- 12 cm
- 48 cm
24 cm
Hint: The diameter is two radii laid end to end: 2 × 12 = 24 cm.
Question 4
A circle has a diameter of 9 cm. What is its circumference? Use 3.14 for π and round to one decimal place.
⭕d = 9 cmanswer boxcm
28.3 cm
Hint: C = π × d ≈ 3.14 × 9 = 28.26. Rounded to one decimal place: 28.3 cm.
Question 5
A circle has a radius of 4 cm. What is its area? Use 3.14 for π and round to one decimal place.
⭕r = 4 cmanswer boxcm²
50.2 cm²
Hint: A = π × r × r ≈ 3.14 × 4 × 4 = 3.14 × 16 = 50.24. Rounded: 50.2 cm².
Question 6
A circle has a diameter of 24 cm. Using 3.14 for π, what is its area?
⭕d = 24 cm- 75.36 cm²
- 37.68 cm²
- 1808.64 cm²
- 452.16 cm²
452.16 cm²
Hint: First find the radius: 24 ÷ 2 = 12. Then A = 3.14 × 12 × 12 = 452.16 cm². (Using the diameter instead of the radius makes the area 4 times too big.)