Answer:
(i) The name of the part of the circle, OQ is a radius
(ii) The radius of the sector QOR is 21 cm
Step-by-step explanation:
The given figure is a sector of the circle O
∵ Any sector of a circle formed from 2 radii and an arc
∴ OQ is a radius
(i) The name of the part of the circle, OQ is a radius
The rule of the length of an arc of a circle is L = [tex]\frac{\alpha }{360}[/tex] × 2 π r, where
- α is the angle of the sector
- r is the radius of the circle
∵ The length of the arc QR is 22 cm
∴ L = 22
∵ The measure of the angle of the arc is 60°
∴ α = 60°
∵ π = [tex]\frac{22}{7}[/tex]
→ Substitute them in the rule above
∵ 22 = [tex]\frac{60}{360}[/tex] × 2 × [tex]\frac{22}{7}[/tex] × r
∴ 22 = [tex]\frac{22}{21}[/tex] r
→ Divide both sides by [tex]\frac{22}{21}[/tex]
∴ 21 = r
(ii) The radius of the sector QOR is 21 cm
