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Radius, diameter, circumference and area

Find circumference and area from a circle’s radius or diameter.

Practice + answer key · 4 pages

Worksheet settings8 questions · 2 columns · A4
Given radius or diameter

The stated length lies in this range. Its label identifies whether it is r or d.

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Radius, diameter, circumference and areaRadius, diameter, circumference and area. Practice. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π.Name __________________________Date _______________Radius, diameter, circumference and areaFind the circumference and area. Leave answers in terms of π.Worked exampleA circle has diameter 10 cm. Find its circumference and area. → Circumference= 10π cm; area = 25π cm²Radius = 10 ÷ 2 = 5 cm.1.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 10 cm.d = 10 cm2.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 3 cm.d = 3 cm3.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 9 cm.d = 9 cm4.Find the circumference and area.Leave answers in terms of π.Circle with a labeled radius of 9 cm.r = 9 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 2mathsprig-1 · mathsprig-v1 · b2eb17f1
Radius, diameter, circumference and areaRadius, diameter, circumference and area. Practice. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π. Find the circumference and area. Leave answers in terms of π.Name __________________________Date _______________Radius, diameter, circumference and areaFind the circumference and area. Leave answers in terms of π.5.Find the circumference and area.Leave answers in terms of π.Circle with a labeled radius of 6 cm.r = 6 cm6.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 11 cm.d = 11 cm7.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 9 cm.d = 9 cm8.Find the circumference and area.Leave answers in terms of π.Circle with a labeled diameter of 2 cm.d = 2 cmMathSprig · mathsprig.site · support@mathsprig.sitePage 2 of 2mathsprig-1 · mathsprig-v1 · b2eb17f1
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Practice + answer key · 4 pages

Geometry

What you’ll practice

Calculate circle circumference and area exactly in terms of π.

Check whether the marked length is the radius or diameter before you start. Use the radius for area and leave π in your answers so they stay exact.

How this skill works

Circumference = 2πr = πd.

Area = πr². If the diagram gives a diameter, divide it by 2 before squaring.

Worked example

A circle has diameter 10 cm. Find its circumference and area.
  1. Radius = 10 ÷ 2 = 5 cm.
  2. Circumference = π × 10 = 10π cm.
  3. Area = π × 5² = 25π cm².

Answer: Circumference = 10π cm; area = 25π cm²

Teaching notes

  • Square the radius, not the diameter.
  • Keep π exact unless a task explicitly asks for an approximation.
Practice questions
  1. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 10 cm.

  2. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 3 cm.

  3. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 9 cm.

  4. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled radius of 9 cm.

  5. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled radius of 6 cm.

  6. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 11 cm.

  7. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 9 cm.

  8. Find the circumference and area. Leave answers in terms of π.

    Circle with a labeled diameter of 2 cm.

Answers and steps
  1. Circumference = 10π cm; area = 25π cm²
    1. Radius = diameter ÷ 2 = 10 ÷ 2 = 5 cm.
    2. Circumference = π × 10 = 10π cm.
    3. Area = π × (5)² = 25π cm².
  2. Circumference = 3π cm; area = 9π/4 cm²
    1. Radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 cm.
    2. Circumference = π × 3 = 3π cm.
    3. Area = π × (1.5)² = 9π/4 cm².
  3. Circumference = 9π cm; area = 81π/4 cm²
    1. Radius = diameter ÷ 2 = 9 ÷ 2 = 4.5 cm.
    2. Circumference = π × 9 = 9π cm.
    3. Area = π × (4.5)² = 81π/4 cm².
  4. Circumference = 18π cm; area = 81π cm²
    1. Diameter = 2 × radius = 2 × 9 = 18 cm.
    2. Circumference = π × 18 = 18π cm.
    3. Area = π × (9)² = 81π cm².
  5. Circumference = 12π cm; area = 36π cm²
    1. Diameter = 2 × radius = 2 × 6 = 12 cm.
    2. Circumference = π × 12 = 12π cm.
    3. Area = π × (6)² = 36π cm².
  6. Circumference = 11π cm; area = 121π/4 cm²
    1. Radius = diameter ÷ 2 = 11 ÷ 2 = 5.5 cm.
    2. Circumference = π × 11 = 11π cm.
    3. Area = π × (5.5)² = 121π/4 cm².
  7. Circumference = 9π cm; area = 81π/4 cm²
    1. Radius = diameter ÷ 2 = 9 ÷ 2 = 4.5 cm.
    2. Circumference = π × 9 = 9π cm.
    3. Area = π × (4.5)² = 81π/4 cm².
  8. Circumference = 2π cm; area = π cm²
    1. Radius = diameter ÷ 2 = 2 ÷ 2 = 1 cm.
    2. Circumference = π × 2 = 2π cm.
    3. Area = π × (1)² = π cm².