Arc length and sector area

1. Find arc length for $r=10$ cm, $\theta =\frac{\pi }{5}$.

   3 marks
2. Find sector area for $r=5$ m, $\theta =1.2$ rad.

   3 marks
3. Find the exact arc for radius 8 cm and angle ${135}^{\circ }$.

   3 marks
4. A sector has radius 7 cm and arc 14 cm. Find angle and area.

   3 marks
5. Find the full perimeter of a sector $r=4$ cm, $\theta =\frac{\pi }{2}$.

   3 marks
6. A 12 m² sector has radius 4 m. Find its angle in radians and degrees to one decimal place.

   3 marks

Equivalent correct methods earn the corresponding marks. Include units where asked.

1. Find arc length for $r=10$ cm, $\theta =\frac{\pi }{5}$.

   3 marks

   $s=\frac{10\pi }{5}$.

   $2\pi \text{cm}$
2. Find sector area for $r=5$ m, $\theta =1.2$ rad.

   3 marks

   $K=\frac{25\left(1.2\right)}{2}=15$.

   15 m².
3. Find the exact arc for radius 8 cm and angle ${135}^{\circ }$.

   3 marks

   ${135}^{\circ }=\frac{3\pi }{4}$; multiply by 8.

   $6\pi \text{cm}$
4. A sector has radius 7 cm and arc 14 cm. Find angle and area.

   3 marks

   $\theta =\frac{14}{7}=2$; $K=\frac{49\left(2\right)}{2}=49$.

   2 rad;49 cm².
5. Find the full perimeter of a sector $r=4$ cm, $\theta =\frac{\pi }{2}$.

   3 marks

   Arc is $\frac{4\pi }{2}=2\pi$; add both radii.

   $8+2\pi \text{cm}$
6. A 12 m² sector has radius 4 m. Find its angle in radians and degrees to one decimal place.

   3 marks

   $12=8\theta$, so $\theta =1.5$.

   $1.5\left(\frac{180}{\pi }\right)=85.9437\dots$.

   $1.5\text{rad}\approx {85.9}^{\circ }$.