Geometry · Surface area & volume · 4.3

Volume of a cylinder.

A cylinder is a stack of circles, so its volume is the circular base area (πr²) times the height: πr²h. Radius 3, height 5: π(9)(5) = 45π.

01 / THE IDEA

See it work.

The figure

See the shape.

r=3h=5

Watch the method

Volume of a cylinder

Volume of a cylinder = πr²h.

1 / 2
1

Volume of a cylinder

Area of the circular base (πr²) times the height.

πr2h\pi r^2 h
2

Substitute

Square the radius, times the height, leave π in.

π(3)2(5)=45π\pi(3)^2(5) = 45π
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.

Stack of circles

Volume = area of the circular base × how tall it is.

Why it works

A pile of coins.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Volume of a cylinder, radius 2, height 3? (leave π)

1

Volume of a cylinder

Area of the circular base (πr²) times the height. π r² h

2

Substitute

Square the radius, times the height, leave π in. π(2)²(3) = 12π

EX 2medium

Volume of a cylinder, radius 8, height 7? (leave π)

1

Volume of a cylinder

Area of the circular base (πr²) times the height. π r² h

2

Substitute

Square the radius, times the height, leave π in. π(8)²(7) = 448π

EX 3hard

Volume of a cylinder, radius 7, height 3? (leave π)

1

Volume of a cylinder

Area of the circular base (πr²) times the height. π r² h

2

Substitute

Square the radius, times the height, leave π in. π(7)²(3) = 147π

04 / COMMON TRAPS

Where students slip.

Trap

Using diameter instead of radius.

Fix

πr² uses the radius.

Trap

Forgetting to square r.

Fix

The base area is π r².

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

Volume of a cylinder, radius 5, height 3? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
C2

Volume of a cylinder, radius 4, height 6? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
C3

Volume of a cylinder, radius 5, height 10? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
C4

Volume of a cylinder, radius 2, height 9? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
Apply

Apply (4)

A1

Volume of a cylinder, radius 7, height 5? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
A2

Volume of a cylinder, radius 2, height 5? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
A3

Volume of a cylinder, radius 2, height 5? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
A4

Volume of a cylinder, radius 6, height 9? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
Extension

Extension (4)

E1

Volume of a cylinder, radius 7, height 4? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
E2

Volume of a cylinder, radius 2, height 5? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
E3

Volume of a cylinder, radius 6, height 8? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.
E4

Volume of a cylinder, radius 5, height 10? (leave π)

Need a hint?
  • Find the base area π r².
  • Multiply by the height.