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7th grade · Math · Unit 5 of 20

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.

New York State Learning Standards learning standard: NY-7.G.4 · the 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 New York

In the New York State Learning Standards, this is unit 5 of 20 in 7th grade Math, after Two-Step Equations and before Probability.

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: New York State Education Department (NYSED)

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 circle's circumference is 97.34 cm. What is its diameter? (Use 3.14 for π.)

    answer boxcm

  2. Question 2

    A round pizza has a diameter of 26 cm. What is the area of its top? Use 3.14 for π and round to one decimal place.

    🍕d = 26 cm

    answer boxcm²

  3. Question 3

    A circle has a diameter of 21 cm. What is its circumference? Use 3.14 for π and round to one decimal place.

    ⭕d = 21 cm

    answer boxcm

  4. Question 4

    About how many times longer is a circle's circumference than its diameter?

    • A little more than 3 times
    • About 4 times
    • A little less than 3 times
    • Exactly 2 times

  5. Question 5

    A circle has a diameter of 20 cm. Using 3.14 for π, what is its area?

    ⭕d = 20 cm
    • 314 cm²
    • 31.4 cm²
    • 62.8 cm²
    • 1256 cm²

  6. Question 6

    A circle has a radius of 20 cm. What is its diameter?

    ⭕r = 20 cm
    • 10 cm
    • 20 cm
    • 80 cm
    • 40 cm

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