Geometry · Perimeter & area · 3.5

Cir- cles.

A circle’s circumference (distance around) is 2πr, and its area (space inside) is πr². For radius 5, the area is π(5)² = 25π. Leaving answers in terms of π keeps them exact.

01 / THE IDEA

See it work.

The figure

See the shape.

r=5

Watch the method

Circles

Circumference = 2πr; Area = πr².

1 / 2
1

Area of a circle

Area is π times the radius squared.

πr2\pi r^2
2

Square the radius

Square r first, then multiply by π.

π(5)2=25π\pi(5)^2 = 25π
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Find the measure.

Type the number — units optional.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

π ties it together

Every circle’s around-and-inside measures use π with the radius.

Why it works

Square the radius for area.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Area of a circle, radius 10? (leave π)

1

Area of a circle

Area is π times the radius squared. π r²

2

Square the radius

Square r first, then multiply by π. π(10)² = 100π

EX 2medium

Area of a circle, radius 7? (leave π)

1

Area of a circle

Area is π times the radius squared. π r²

2

Square the radius

Square r first, then multiply by π. π(7)² = 49π

EX 3hard

Area of a circle, radius 5? (leave π)

1

Area of a circle

Area is π times the radius squared. π r²

2

Square the radius

Square r first, then multiply by π. π(5)² = 25π

04 / COMMON TRAPS

Where students slip.

Trap

Mixing up the formulas.

Fix

Area uses r²; circumference uses r.

Trap

Forgetting to square r for area.

Fix

Area is π r², not π r.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Area of a circle, radius 10? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
C2

Area of a circle, radius 8? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
C3

Area of a circle, radius 5? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
C4

Area of a circle, radius 4? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
Apply

Apply (4)

A1

Area of a circle, radius 7? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
A2

Area of a circle, radius 6? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
A3

Area of a circle, radius 8? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
A4

Area of a circle, radius 7? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
Extension

Extension (4)

E1

Area of a circle, radius 10? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
E2

Area of a circle, radius 3? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
E3

Area of a circle, radius 10? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.
E4

Area of a circle, radius 5? (leave π)

Need a hint?
  • Area uses r².
  • Leave the answer in terms of π.