Arc Lengths & Sector Areas Flashcards

All 5 cards in this deck

What is the formula for the arc length of a sector of angle $\theta$?

e.g. angle $90^\circ$, radius $6$ cm

Arc length $= \frac{\theta}{360} \times 2\pi r$

$\frac{90}{360} \times 2\pi \times 6 = 3\pi$ cm

What is the formula for the area of a sector of angle $\theta$?

e.g. angle $90^\circ$, radius $6$ cm

Area $= \frac{\theta}{360} \times \pi r^2$

$\frac{90}{360} \times \pi \times 6^2 = 9\pi$ cm$^2$

What lengths make up the perimeter of a sector?

e.g. sector of radius $5$ cm with arc length $7$ cm

The arc length plus the two radii.

$7 + 5 + 5 = 17$ cm

What are the steps to find the angle of a sector from its arc length?

e.g. arc length $4\pi$ cm, radius $8$ cm

1. Full circumference: $2\pi \times 8 = 16\pi$ cm

2. Fraction of the circle: $4\pi \div 16\pi = \frac{1}{4}$

3. Multiply by $360$: angle $= 90^\circ$

True or false? A sector with an angle of $60^\circ$ has an arc length equal to $\frac{1}{6}$ of the circumference.

True. $\frac{60}{360} = \frac{1}{6}$ of the whole circle.