Getting the angle fraction upside down
"The Fraction Flip"
The Mistake in Action
Find the area of a sector with radius 8 cm and angle 45°.
Wrong: Area = $\frac{360}{45} \times \pi \times 8^2 = 8 \times 64\pi = 512\pi$ cm²
Why It Happens
Students set up the fraction as $\frac{360}{\theta}$ instead of $\frac{\theta}{360}$.
The Fix
The sector is a fraction of the whole circle, where the fraction = $\frac{\theta}{360}$.
45° is less than 360°, so the fraction should be less than 1.
$$\text{Sector area} = \frac{45}{360} \times \pi \times 8^2 = \frac{1}{8} \times 64\pi = 8\pi = 25.1 \text{ cm}^2$$
Quick check: A sector should be smaller than the full circle, not 8 times bigger!
Spot the Mistake
Can you identify where this student went wrong?
Sector with angle 45°
$\frac{360}{45} \times \pi r^2$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: