Can anyone teach mee.....................

Mathematics

1 answer:

andrew11 [14]3 years ago

5 0

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 = $\frac{\alpha }{360}$ × 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 = $\frac{22}{7}$

→ Substitute them in the rule above

∵ 22 = $\frac{60}{360}$ × 2 × $\frac{22}{7}$ × r

∴ 22 = $\frac{22}{21}$ r

→ Divide both sides by $\frac{22}{21}$

∴ 21 = r

(ii) The radius of the sector QOR is 21 cm

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