Learn · Numeracy · 5 min

Circles & cylinders, from scratch

Circles bring in one special number — π (“pi”). Get these words first:

radiuscentre to the edge
diameterall the way across = 2 × radius
π ≈ 3.14the distance around is always ≈ 3.14 × the diameter

See it: π links a circle’s width to its distance around

Radius (centre to edge): 5

diameter = 2 × 5 = 10
circumference = 2 × π × 5 ≈ 31.4
area = π × 5² ≈ 78.5

The two circle formulas

Circumference (around) = π × diameter = 2 × π × radius.
Area (inside) = π × radius².
Tip: use π ≈ 22/7 when the radius is a multiple of 7 — the answer comes out neat.

Now go 3D — the cylinder

A cylinder is just a circle given a height. So its volume is the circle’s area, stacked up.

See it: a cylinder is a circle stacked up

Radius: 4

Height: 6

Volume = π × 4² × 6 ≈ 302
= area of the circle base (π × 4²) × height (6)

The one move: base area × height

Volume of a cylinder = π × radius² × height — work out the circle base (π × r²), then multiply by the height. Answer in cubic units (cm³).

Tips & tricks

Circumference (distance around)

π × diameter = 2 × π × radius

Area of a circle

π × radius² (square the radius, then × π)

Cylinder volume

π × radius² × height (circle base × height)

Which π to use

π ≈ 3.14 normally; π ≈ 22/7 when the radius is a multiple of 7.

Quick sanity check

π is just over 3, so the way around is a bit more than 3 × the width (diameter).

Now you try — 0/3

1. A circle has a radius of 5 cm. What is its diameter (in cm)?

2. Using π ≈ 22/7, what is the circumference of a circle with radius 7 cm?

3. Using π ≈ 3, roughly what is the AREA of a circle with radius 10 cm (in cm²)?

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