Question

III Answer the following (3 x 3m = 9m)
15. Draw a circle with the radios 5.5cm. From a point scm away from its center, construct a pair of tangents to the circle and measure their lengths.
16. A car has two wipers which do not overlap. Each wiper has a blad of length 25cm sweeping through an angle 1150. Find the total Area cleaned at each sweep of the blades ​

Answer 1

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1) Draw a circle of radius 5 cm.

2) Draw horizontal radius OQ.

3) Draw angle 120°

from point O. Let the ray of angle intersect the circle at point R.

4) Now draw 90° from point Q.

5) Draw 90° from point R.

6) Where the two arcs intersect, mark it as point P.

Therefore, PQ and PR are the tangents at an angle of 60°

Total area cleaned by 2 wipers

=2× area cleaned by 1 wiper

=2× area of sector with 115°

=2× 360×πr²

=2× 115°/360°× 22/7× 25²

Therefore area cleaned by wipers = 158125/126cm² =1254.96

Answer 2

SOLUTION

Q. 16

Car has two vipers , let ø be the angle which is covered by viper

Given that ø= 115⁰ and length of viper ( r) = 25cm

Thus it makes a sector which is inclined by 115⁰,

⇒Area swept by the car viper = ø/360⁰×π r²

⇒Area swept by the car viper = 115⁰/360⁰×22/7×25×25

⇒Area swept by the car viper = 23⁰/72²×22/7×25×25=627.48 cm²

⇒Area swept by two vipers of the car =1254.96 cm²

MORE TO KNOW

• Area of sector = ø/360⁰πr²
• Area of segment = area of sector-area of triangle = ø/360⁰πr²-1/2 r² sin ø
• Area of quadrant = 1/4 πr²
• Area of semicircle= 1/2 πr²

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