Using diameter instead of radius in arc/sector formulas
"The D for R Disaster"
The Mistake in Action
A sector has diameter 10 cm and angle 72°. Find the arc length.
Wrong: Arc = $\frac{72}{360} \times 2\pi \times 10 = \frac{1}{5} \times 20\pi = 4\pi$ cm
Why It Happens
Students use the diameter value directly without halving it to get the radius.
The Fix
The formula uses radius, not diameter!
Diameter = 10 cm, so Radius = 5 cm
Arc length = $\frac{72}{360} \times 2\pi \times 5 = \frac{1}{5} \times 10\pi = 2\pi = 6.28$ cm
Always check: Does the question give diameter or radius?
Spot the Mistake
Can you identify where this student went wrong?
Diameter 10 cm
Arc = $\frac{72}{360} \times 2\pi \times 10$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: