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7th grade · Math · Unit 5 of 16

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.

Arizona Academic Standards learning standard: 7.G.B.4 · circumference and area of circles

How we explain it

Children can open this short lesson before they practice.

  1. The radius goes from the center to the edge. The diameter goes all the way across: d = 2r.
  2. Circumference (the distance around) is C = π × d.
  3. 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 Arizona

In the Arizona Academic Standards, this is unit 5 of 16 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: Arizona Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A bike wheel has a diameter of 60 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 = 60 cm

    answer boxcm

  2. Question 2

    A circle has a diameter of 36 cm. What is its radius?

    ⭕d = 36 cm
    • 9 cm
    • 18 cm
    • 36 cm
    • 72 cm

  3. Question 3

    A circle has a diameter of 10 cm. Using 3.14 for π, what is its area?

    ⭕d = 10 cm
    • 78.5 cm²
    • 314 cm²
    • 31.4 cm²
    • 15.7 cm²

  4. Question 4

    A circle's circumference is 113.04 cm. What is its diameter? (Use 3.14 for π.)

    answer boxcm

  5. Question 5

    A circle has a radius of 6 cm. What is its area? Use 3.14 for π and round to one decimal place.

    ⭕r = 6 cm

    answer boxcm²

  6. Question 6

    A circle has a diameter of 42 cm. What is its circumference? Use 3.14 for π and round to one decimal place.

    ⭕d = 42 cm

    answer boxcm

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