Geometry · Apply · 5.3

Wheels & gardens.

Round things — a circular garden, a pizza, a wheel — use circle formulas. The space inside is the area πr²; the distance around is the circumference 2πr. A garden of radius 7 has area 49π.

01 / THE IDEA

See it work.

The figure

See the shape.

r=7

Watch the method

Wheels & gardens

Round region → area πr²; rim → circumference 2πr.

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(7)2=49π\pi(7)^2 = 49π
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.

Round measurements

Anything circular uses π with the radius for area and circumference.

Why it works

Inside vs around.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

EX 2medium

Area of a circle, radius 11? (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(11)² = 121π

EX 3hard

Area of a circle, radius 4? (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(4)² = 16π

04 / COMMON TRAPS

Where students slip.

Trap

Using a diameter as the radius.

Fix

The radius is half the diameter.

Trap

Mixing area and circumference.

Fix

Inside is π r²; around is 2 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 5? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
C2

Area of a circle, radius 5? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
C3

Area of a circle, radius 7? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
C4

Area of a circle, radius 9? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
Apply

Apply (4)

A1

Area of a circle, radius 7? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
A2

Area of a circle, radius 2? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
A3

Area of a circle, radius 9? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
A4

Area of a circle, radius 9? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
Extension

Extension (4)

E1

Area of a circle, radius 4? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
E2

Area of a circle, radius 11? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
E3

Area of a circle, radius 12? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.
E4

Area of a circle, radius 11? (leave π)

Need a hint?
  • Inside a circle → area π r².
  • Square the radius.