X, Mathematics, Areas Related To Circles
X, Mathematics, Areas Related To Circles
X, Mathematics, Areas Related To Circles
1. The area of a sector whose perimeter is four times its radius r units, is
2
a) r
sq units b) 2r2 sq. units
2
c) r2 sq. units d) r
sq units
4
2. A car has two wipers which do not overlap. Each wiper has a blade of length 42 cm sweeping through an angle of 120o.
Find the total area cleaned at each sweep of the blades.
3. If the area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm2, then find it's radius
a) 10 cm b) 16 cm
c) 12 cm d) 8 cm
4. A chord of a circle subtends an angle of 60o at the centre. If the length of the chord is 100 cm, find the area of the major
segment.
5. What is the perimeter of a sector of a circle whose central angle is 90° and radius is 7 cm?
6. Find the area of a sector of circle of radius 21 cm and central angle 120°.
7. Find the area of a sector of a circle of radius 28 cm and central angle 45°.
8. The areas of two sectors of two different circles with equal corresponding arc lengths are equal. Is this statement true?
Why?
9. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
10. The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35
minutes.
11. The perimeter of a certain sector of a circle of radius 6.5 cm is 31 cm. Find the area of the sector.
12. From a circular piece of carboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the
remaining portion nearest hundredth centimeters. (Take π = 22/7).
13. What is the length (in terms of π) of the arc that subtends an angle of 36° at the centre of a circle of radius 5 cm?
14. Write the formula for the area of a segment in a circle of radius r given that the sector angle is θ (in degrees).
15. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of distances travelled by their tips
in 24 hours, (use π = 3.14).
16. The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector.
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By Joginder Sir
17. A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60° at its centre. Find the
radius of the circle.
18. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment. [Use π =
3.14.]
19. The length of an arc of a circle, subtending an angle of 54° at the centre is 16.5 cm. Calculate the radius, circumference
and area of the circle.
20. ABCD is a field in the shape of a trapezium, AD II BC, ∠ABC = 90° and ∠ADC = 60°. Four sectors are formed with
centres A, B, C and D, as shown in the figure. The radius of each sector is 14 m. Find the following:
25. Below figure shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠ AOB = 90°,
calculate
i. the height of the tunnel
ii. the perimeter of the cross-section
iii. the area of the cross-section
26. Area of a sector of a circle of radius 36 cm is 54π cm .Find the length of the corresponding arc of sector.
2
27. A sector is cut-off from a circle of radius 21 cm. The angle of the sector is 120°. Find the length of its arc and the area.
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By Joginder Sir
28. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of the distances travelled by their
tips in two days.
29. A chord of a circle of radius 10cm subtends a right angle at the center. Find the area of the corresponding: (Use π = 3.14)
i. minor sector
ii. major sector
iii. minor segment
iv. major segment
30. Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending angle of 90° at
the centre.
31. An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the
centre O of the pulley until it is at P, 10 cm from O. Find the length of the belt that is in contact with the rim of the
pulley. Also, find the shaded area.
32. A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making
the designs at the rate of ₹ 0.35 per cm 2. (use √3 = 1.7)
–
33. Assertion (A): In a circle of radius 6 cm, the angle of a sector 60o. Then the area of the sector is 18 6
7
cm
2
.
Reason (R): Area of the circle with radius r is πr .2
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
square is 1946cm2.
Reason (: Angle described by a minute hand in 60 minutes = 360o.
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
2
2
r sin θ
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
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By Joginder Sir
36. Assertion (A): Area of a sector of a circle whose length of arc is 2l and length of the corresponding radius is 2r is given
by 2lr.
Reason (R): Area of a sector of a circle = Length of arc × length of radius × 1
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.
Question No. 37 to 40 are based on the given text. Read the text carefully and answer the questions:
To find the polluted region in different areas of Dwarka (a part of Delhi represented by the circle given below) a survey was
conducted by the students of class X. It was found that the shaded region is the polluted region, where O is the centre of the
circle.
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By Joginder Sir