CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set C

Case Study Based Questions

I. A human chain is to be formed in concentric form of radius 56 m and 63 m at India Gate. But the organiser has some problems, he wants you to solve his problems. Give answer to his questions by using information given in the questions:

Question. The circumference of circular chain of radius 56 m is
(a) 352 m
(b) 176 m
(c) 704 m
(d) 88 m
Answer : A

Question. The area covered by circular chain of radius 56 m is
(a) 5544 m²
(b) 3850 m²
(c) 9856 m²
(d) 12474 m²
Answer : C

Question. If each person is given two metres of space to stand, find how many persons can be accomodated in the chain of radius 56 m.
(a) 126 persons
(b) 176 persons
(c) 156 persons
(d) 186 persons
Answer : B

Question. He wants to include one more concentric circle with a radius of 63 m, the circumference of the new circle will be
(a) 156 m
(b) 396 m
(c) 176 m
(d) 288 m
Answer : B

Question. How many persons can accomodate on the new circle if each person needs 2 metres of space?
(a) 198 persons
(b) 156 persons
(c) 176 persons
(d) 186 persons
Answer : A
 

II. A square park has each side of 100 m. At each corner of the park, there is a flower bed in the form of a quadrant of radius 14 m as shown in given figure.

Answer the question from (1) to (5):

Question. Area of each quadrant is
(a) 145 m²
(b) 154 m²
(c) 415 m²
(d) 514 m²
Answer : B

Question. Area of 4 quadrants is
(a) 616 m²
(b) 166 m²
(c) 661 m²
(d) 510 m²
Answer : A

Question. Area of park with bed roses is
(a) 10,000 m²
(b) 1000 m²
(c) 100 m²
(d) 10 m²
Answer : A

Question. Area of park without bed roses is
(a) 9834 m²
(b) 9384 m²
(c) 9483 m²
(d) 9348 m²
Answer : B

Question. Angle of a quadrant is equal to
(a) 70°
(b) 80°
(c) 90°
(d) 45°
Answer : C
 

III. A student of class-X^th decided to create a model of a circular wall clock and try to paste the numbers from 1 to 12 on its dial. But he is facing some problems.
Give solutions to his problems by looking at the figure.

Question. The angle between points showing hour is
(a) 15°
(b) 30°
(c) 45°
(d) 60°
Answer : A

Question. What is the angle made at the centre between 12 and 3?
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer : D

Question. Find the area covered by minute hand of a clock from 12 to 3 if the radius of the clock is 14 cm.
(a) 164 sq. cm
(b) 77 sq. cm
(c) 154 sq. cm
(d) 308 sq.cm
Answer : C

Question. The formula used in finding the area of sector with radius r and angle at the centre q is
(a) πr²θ/360°
(b) πr²θ/180°
(c) 2πrθ/180°
(d) πrθ/360°
Answer : A

Question. The arc length between the region 12 and 3 if the radius of the clock is 14 cm.
(a) 22 cm
(b) 44 cm
(c) 66 cm
(d) 88 cm
Answer : A

1) A bicycle wheel makes 5000 revolution in moving 11 km. find the diameter of the wheel (d = 70 cm)

2) The radius of the wheel of a bus is 70cm, how many revolutions per minute must a wheel make in order to move at a speed of 66 km/h (250)

3) A wheel has diameter 84cm. Find how many complete revolutions must it make to cover 792 metres (300)

4) In the figure o is the centre of a circle. The area of sector OAPB is 5/18 of the area of the circle. Find x (100˚) A B p

5) Area of a sector of a circle is 1/6 to the area of circle. Find the degree measure of its minor arc (60˚)

6) Area of a sector of a circle of radius 14cm is 154 cm2 . Find the length of the corresponding arc of the sector (22 cm)

7) If the diameter of a semi circle protractor is 14 cm. Find its perimeter (36cm)

8) The circumference of a circle A is 132cm. It is equal to the sum of the circumference of two circles B & C, the radius of the circle

B is 14cm. Find the radius of circle C. (r = 7 cm)

9) The area of quadrant is 154sq cm. Find its perimeter. (50 cm)

10) Two circles touch externally. The sum of their areas is 130π sq.cm and the distance between their centres is 14cm. Find the radii of the Circles (11cm ,3cm)

11) Find the area of a quadrant of a circle whose circumference is 44cm (38.5cm2)

12) The perimeter of a sheet of paper in the shape of a quadrant of a circle is 75 cm. Find its area (346.5 sqcm)

13) If the perimeter of the protractor is 72cm, calculate its area ( 308cm2)

14) A circular disc of 6cm radius is divided into 3 sectors with central angles 120˚, 150˚and 90˚.Find the ratio of the areas of 3 Sectors (4: 5: 3)

15) The difference between circumferences and diameter of a circle is 105 cm. Find the radius of the circle (24.5 cm)

16) Find the area of a major sector of a circle of diameter 42 cm and central angle is 60˚ (1155cm2)

17) If the area and circumference of a circle are numerically equal, then find the radius of the circle (2cm)

18) The length of a rope by which a cow is tethered is increased from 16m to 23m. How much additional area can the cow graze? Now (π =22/7) (2.38 Ѳm2)

19) What will be the increase in area of circle if its radius is increased by 40% (96%)

20) An arc of a circle is of length 5π cm and the sector it bounds has an area of 20π cm2 . Find the radius of the circle (8cm)

21) The circumference of a circle exceeds the diameter by 16.8cm. Find the radius of circle (3.92cm)

22) The area enclosed between two concentric circles is 770 sq cm. If the radius of outer circle is 21cm. Find the radius of the inner circle. (14 cm)

23) The length of the minute hand of a clock is 7cm. How much area does it sweep in 20minutes (154/3 cm2)

24) The perimeter of a sector of a circle of radius 5.2cm is 16.4cm.Find the area of sector (15.6cm2)

25) Given a circle of radius 9cm, and the length of the chord AB of a circle is 9√3 cm, find the area of the sector formed by arc AB. (84. 85 cm2)

26) Length of minor arc of a circle of radius 10 cm is 14cm. Find the area of minor sector of a circle. (70cm2)

27) A chord 10 cm long is drawn in a circle of radius V50 cm. Find the area of minor segment (14. 285 cm2)

28) A chord AB of a circle of radius 14cm makes a right angle at the centre of the circle. Find the area of the minor segment. (π = 22/7) (56 cm2)

29) A chord of a circle of radius 14cm subtends an angle of 120˚ at the centre Find the area of the corresponding minor segment of The circle (π = 22/7, √3 = 1.73) (120.56 cm2 )

30) From a thin metallic piece, in the shape of a trapezium ABCD in which AB II CD and ∟BCD = 90˚, a quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2cm, calculate the area of the remaining (shaded) part of the metal sheet (π = 22/7)

Please click the below link to access CBSE Class 10 Mathematics Worksheet - Areas related to Circles (2)