### Mensuration Ex. No. 6.1

1. The diameter of a circle is 10 cm. Find the length of the arc, when the corresponding central angle is given below. (π = 3.14)

i. 1440 [

ii. 450 [

iii. 2700 [

iv. 1800 [

2. Find the angle subtended at the centre of a circle by an arc, for the following.

i. radius of circle = 5.5 cm, length of arc = 6.05 cm (π = 22/7)

ii. radius of circle = 20 cm, length of arc = 78.50 cm (π = 3.14)

3. The radius of the circle is 7 cm and m(arc RYS)  = 600, with the help of the fig. 6.8. answer the following questions.

4. The radius of a circle is 7 cm. Find area of the sector of this circle if the corresponding angle is

5. An arc of a circle having measure 360 has length 176m. Find the circumference of the circle.

6. An arc of length 4π cm subtends an angle of 400 at the centre. Find the radius and the area of the sector formed by this arc. [Solution]

7. If the area of the minor sector is 392.5 sq. cm. and the corresponding central angle is 720, find the radius. (π = 3.14) [Solution]

8. Find the area of sector whose arc length and radius are 10cm and 5 cm respectively. [Solution]

9. If the area of minor sector of a circle with radius 11.2 cm is 49.28 sq. cm., find the measure of the arc. [Solution]

10. Find the length of the arc of a circle with radius 0.7 m and area of the sector is 0.49 sq. m. [Solution]

11. Two arcs of the same circle have their lengths in the ratio 4:5. Find the ratio of the areas of the corresponding sectors. [Solution]

12. Adjoining figure depicts a racing track whose left and right ends are semicircular. The distance between two inner parallel lines segments is 70 m and they are each 105 m long. If the track is 7m wide, find the difference in the lengths of the inner edge and outer edge of the track. [Solution]

13. A horse is tied to a pole fixed at one corner of a 30m × 30m square field of a grass by a 10m long rope. (π = 3.14)
(i) Find the area of that part of the field in which the horse can graze. [Refer Fig. 6.10 (i) ]

(ii) What will be the area of the field in which the horse can graze, if the pole was fixed at the middle of the side? [Solution