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 [Solution]

ii. 450 [Solution]

iii. 2700 [Solution]

iv. 1800 [Solution]

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) [solution]

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

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. [solution]

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

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

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