1. In the given figure, the shape of the top of a table is that a sector of a circle with centre O and 2 AOB = 90°. If AO = OB = 42 cm, then find the perimeter of the top of the table. [Use = ]
2. In the given figure, the area of the shaded region between two concentric circles is 286 cm2. If 2 the difference of the radii of the two circles is 7 cm, find the sum of their radii. [Use = ]
3. The minute hand of a clock is cm long. Find the area described by the minute hand on the 2 face of the clock between 7.00 am and 7.05 am. [Use = ]
4. A wire is looped in the form of a circle of radius 28 cm. It is reverted into a square form. 2 Determine the side of the square. [Use = ]
5. In the given figure, sectors of two concentric circles of radii 7 cm and 3.5 cm are given. Find the 2 area of the shaded region. [Use = ]
6. OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of 2 the circle is 10 cm, find the area of the rhombus.
7. A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one 2 corner by a rope 21 m long. On how much area can it graze? 8. The diameter of a wheel of a bus is 90 cm which makes 315 revolutions per minute. Determine 2 its speed in km/h. [Use = ]
9. In given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn 2 with AO and OB as diameters. If AB = 28 m, find the perimeter of the shaded region. [Use = ]
10. A playground is in the form of a rectangle having semicircles on the shorter sides. Find its area 2 when the length of the rectangular portion is 80 m and the breadth is 42 m.
11. A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m 2 have been cut. Find the area of the remaining part.
12. The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in three 2 minutes. [Use = 22/7]
13. A circular grassy plot of land 42 m in diameter has a path 3.5 m wide running round it on the 2 outside. Find the cost of gravelling the path at the rate of 4 per square metre.
14. The diameter of the wheel of a bus is 140 cm. How many revolutions per minute must the wheel 2 make in order to keep a speed of 66 km/h?
15. The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector. 2
16. The measure of the minor arc of a circle is 1/5 of the measure of the corresponding major arc. If 2 the radius of the circle is 10.5 cm, find the area of the sector corresponding to the major arc. [ = 22/7]
17. OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region. 2 [Use = ] 18. Find the area of the segment of a circle, if angle of the sector is 90° and the radius of the circle is 2 21 cm.
19. Find the area of the shaded region in figure, if AC = 24 cm, BC = 10 cm and O is the centre of the 2 circle.
20. A square park has each side of 100 m. At each corner of the park, there is a flower bed in the 2 form of a quadrant of radius 14 m as shown in the given figure. Find the area of the remaining part of the park. [Take = 22/7]
21. In figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm. To 2 intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region. [Use = 3.14].
22. The areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume 2 is 9000 cu. cm, find the length of the shortest side.
23. In fig., the shape of the top of a table in restaurant is that of a sector of a circle with centre O and 3 BOD = 90°, if BO = OD = 60 cm find: (i) the area of the top of the table (ii) the perimeter of the table top. [Take = 3.14]
24. In fig., ABC is a right-angled triangle, right-angled at A. Semicircles are drawn on AB, AC and BC 3 as diameters. Find the area of the shaded region. 25. In the fig., ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as 3 diameter. Find the area of the shaded region.
26. A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing 3 would be 2640 at the rate of 12 per metre. Then the field is to be thoroughly ploughed at the cost of 0.50 per m2. What is the amount required to plough the field?
27. Find the number of revolutions made by a circular wheel of area 1.54 m2 in rolling a distance of 3 176 m.
28. Find the area of the major segment APB, in figure of a circle of radius 35 cm and AOB = 90°. 3 [Use = ]
29. In the middle of a tile there is a coloured circular portion as shown. The radius of coloured 5 position is 21 cm. The uncoloured portion (unshaded portion) subtends angle 60° at the centre as shown OA is radius.
Answer the question based on above
(a) What is the length of the arc AB?
(b) What is the area of minor sector AOB?
(c) What is the area of major sector AOB?
(d) Find the area of corresponding minor segment corresponding to chord AB?
(e) Find the area of corresponding major segment corresponding to chord AB? 30. A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a 5 dress, blouse or coat.
Designs of some brooch are shown below. Observe them carefully.
Design A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.
Design B: Brooch b is made two colours_Gold and silver. Outer part is made with Gold. The circumference of silver part is 44 mm and the gold part is 3 mm wide everywhere.
Refer to Design A
(a) The total length of silver wire required is
(i) 180 mm (ii) 200 mm
(iii) 250 mm (iv) 280 mm
(b) The area of each sector of the brooch is
(i) 44 mm2 (ii) 52 mm2
(iii) 77 mm2 (iv) 68 mm2
Refer to Design B
(c) The circumference of outer part (golden) is
(i) 48.49 mm (ii) 82.2 mm (iii) 72.50 mm (iv) 62.86 mm
(d) The difference of areas of golden and silver parts is
(i) 18 π (ii) 44 π (iii) 51 π (iv) 64 π
(e) A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80p mm ?
(i) 2 (ii) 3 (iii) 4 (iv) 5
31. A plot is in the form of a rectangle ABCD. A semicircular portion is shown on side BC. The 5 semicircular portion is planted with sunflower plants and remaining portion is used for planting vegetables.
Answer the questions based on above
(a) Find the area of plot used for sunflower plants.
(b) Find the area of plot used for vegetables.
(c) If all the sunflower plants should be planted in sector with center angle 60° then what will be the radius of the sector?
(d) What will be the radius of circle, if circumference of circle is same as perimeter of given rectangular plot?
(e) If side BC be looped in the form of a circle then what will be the radius of circle?
32. The circumference of a circle is the product of the constant π and diameter of a circle. The 5 circumference is the length of complete arc of the circle.
Circumference of circle = πd
A man starts running from point A and reaches the same point after completing one complete round of a circle. The distance covered by him is the circumference of a circle. The region inside the boundary is area of circle.
Answer the questions based on above
(a) The circumference of two circles are in the ratio 1 : 4 them ratio of their areas is
(i) 16 : 1 (ii) 1: 16 (iii) 1 : 2 (iv) 2 : 1
(b) The ratio of the area of in circle and circumcircle of a square is
(i) 2 : 1 (ii) 1 : 9 (iii) 1 : 3 (iv) 1 :
(c) The perimeter of a semicircular protractor is 66 cm, then radius of protractor is
(i) cm (ii) 3 cm (iii) cm (iv) 11 cm
(d) If area of circle is numerically equal to two times is circumference, then radius of circle is
(i) 0 cm (ii) 2 cm (iii) 4 cm (iv) 6 cm
(e) The area of quadrant of a circle whose circumference is 44 cm
