Question

NO LINKS!!! Find the arc measure and arc length of AB. Then find the area of the sector ABQ.​

Answer 1

Arc Measure: equal to the measure of its corresponding central angle.

Formulas

`\textsf{Arc length}=2 \pi r\left((\theta)/(360^(\circ))\right)`

`\textsf{Area of a sector of a circle}=\left((\theta)/(360^(\circ))\right) \pi r^2`

`\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}`

Question 39

Given:

• r = 7 in
• 
  `\theta` = 90°

Substitute the given values into the formulas:

Arc AB = 90°

`\textsf{Arc length of AB}=2 \pi (7) \left((90^(\circ))/(360^(\circ))\right)=3.5 \pi=11.00\:\sf in\:(2\:d.p.)`

`\textsf{Area of the sector AQB}=\left((90^(\circ))/(360^(\circ))\right) \pi (7)^2=(49)/(4) \pi=38.48\:\sf in^2\:(2\:d.p.)`

Question 40

Given:

• r = 6 ft
• 
  `\theta` = 120°

Substitute the given values into the formulas:

Arc AB = 120°

`\textsf{Arc length of AB}=2 \pi (6) \left((120^(\circ))/(360^(\circ))\right)=4\pi=12.57\:\sf ft\:(2\:d.p.)`

`\textsf{Area of the sector AQB}=\left((120^(\circ))/(360^(\circ))\right) \pi (6)^2=12 \pi=37.70\:\sf ft^2\:(2\:d.p.)`

Question 41

Given:

• r = 12 cm
• 
  `\theta` = 45°

Substitute the given values into the formulas:

Arc AB = 45°

`\textsf{Arc length of AB}=2 \pi (12) \left((45^(\circ))/(360^(\circ))\right)=3 \pi=9.42\:\sf cm\:(2\:d.p.)`

`\textsf{Area of the sector AQB}=\left((45^(\circ))/(360^(\circ))\right) \pi (12)^2=18 \pi=56.55\:\sf cm^2\:(2\:d.p.)`