#24
Top 50 Mistake
Using diameter instead of radius in circle formulas
"The D-R Disaster"
The Mistake in Action
A circle has diameter 10cm. Find its area.
Wrong: $A = \pi r^2 = \pi \times 10^2 = 100\pi = 314.16\text{cm}^2$
Why It Happens
Students see "10cm" and plug it straight into the formula without checking if it's the radius or diameter.
The Fix
Always check: Does the question give you radius or diameter?
- Radius = distance from centre to edge
- Diameter = distance across the whole circle = 2 ร radius
If given diameter 10cm, then radius = 5cm.
$$A = \pi r^2 = \pi \times 5^2 = 25\pi = 78.54\text{cm}^2$$
The wrong answer (100ฯ) is 4 times too big!
Spot the Mistake
Can you identify where this student went wrong?
A circle has diameter 10cm. Find its area.
$A = \pi r^2 = \pi \times 10^2$
$= 100\pi = 314.16\text{cm}^2$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: