The areas of common shapes
The area of the disc
The disc, a surface
A disc is the surface bounded by a circle (the circle is the outline; the disc is the filled-in area inside it). So when we ask for ‘the area of the disc’, we are referring to the area inside the circle.
The formula
A = π × r²
where r is the radius of the disc. Note: this is r squared, not 2 × r!
Example
For a disc with radius r = 4 cm: A = π × 4² = 3.14 × 16 = 50.24 cm²
For a disc with a diameter d = 6 cm, you must first calculate the radius: r = d/2 = 3 cm, then: A = 3.14 × 3² = 3.14 × 9 = 28.26 cm²
Summary: circle vs disc
| Quantity | Shape | Formula |
|---|---|---|
| Perimeter (circumference) | Circle (outline) | 2 × π × r |
| Area | Disc (surface area) | π × r² |
Common pitfalls
The most common mistake is forgetting to square the radius, calculating π × r instead of π × r². Another pitfall: using the diameter directly in the area formula (A = π × d² is incorrect; you must first divide the diameter by 2 to obtain the radius).