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Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

2023


Q1: What is the area of a semi-circle of diameter 'd' ?
(a) 1/16πd2
(b) 1/4πd2
(c) 1/8πd2
(d) 1/2πd2        [2023, 1 Mark]
Ans:
(c)
Given diameter of semi circle = d

Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles∴ Radius, r = d/2
Area of semi circle
 = Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesClass 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

Q2: Case Study : Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a bill, which will have adequate space for parking.

Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesAfter survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats. Based on the above information, answer the following questions:

(i) What is the total perimeter of the parking area ? 
(ii) (a) What is the total area of parking and the two quadrants?

OR

(b) What is the ratio of area of playground to the area of parking area ?
(iii) Find the cost of fencing the playground and parking area at the rate of ? 2 per unit.    [2023, 4,5,6 Mark]

Ans: (i) Length of play ground . AB = 14 units, Breadth of play ground. AD = 7 units
Radius of semi - circular part is 7/2 units
Total perimeter of parking area = πr + 2r

Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 11 + 7 = 18 Units
(ii) (a): Area of parking = πr2 / 2
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 19.25 sq. units
Area of two quadrants (I) a n d [II) =1/2 x 1/4 x πr2
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 6.29 sq. units
Total area of parking and two quadrant
= 19.25 + 6.29
= 25.54 sq. units

Q3: A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.      [2023, 4,5,6 Mark]
Ans: Here, radius t(r) = 14 cm and  Sector angle (θ) = 60°
∴ Area of the sector
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

= 102.67 cm2
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesSince ∠O = 60° and OA = OB = 14 cm
∴ AOB is an equilateral triangle.
⇒ AS = 14 cm and ∠A = 60°
Draw OM ⊥ AB.
In ΔAMO
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Now,
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Now, area of the minor segment= (Area of minor sector) - (ar ΔAOB)
= 102.67 - 84.87 cm2 
= 17.8 cm2
Area of the major segment
= Area of the circle - Area of the minor segment  
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

= (616 - 17.8) cm= 598.2 cm2

2022


Q1: The area swept by 7 cm long minute band of a clock in 10 minutes is
(a) 77 cm2
(b) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

(c) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
(d) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles        [2022, 1 Mark]
Ans: (d)
Angle formed by minute hand of a clock in 60 minutes = 360°
∴ Angle formed by minute hand of a clock in 10 minutes = 10/60 x 360° = 60°
Length of minute hand of a dock = radius = 7 cm
∴ Required area
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

Q2: Given below is the picture of the Olympic rings made by taking five congruent circles of radius 1 cm each, intersecting in such a way that the chord formed by joining the point of intersection of two circles is also of length 1 cm. Total area of all the dotted regions assuming the thickness of the rings to be negligible isClass 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles(a) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
(b) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
(c) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
(d) Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles        [2022, 1 Mark]
Ans: (d)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesLet O be the centre of the circle. So. OA = OB = AB = 1 cm
So ΔOAB is an equilateral triangle.
∴ ∠AOB = 60°

∴  Required area = 8 x area of one segment with r = 1 cm,θ = 60°

= 8 x  (area of sector - area of ΔAOB)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

2021

2020

Q1: A piece of wire 22 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. [Use π = 22/7]       [2020, 2 Marks]
Ans: Let AB be the wire of length 22 cm in the form of an art of a circle so blending an ∠AOB - 60° at centre O.Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles∵ Length of arc = Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 21 cm
Hence, radius of the circle is 21cm.

2019


Q1: A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle 120°. Find the total area cleaned at each sweep of the blades. (Take π = 22/7)       [2019, 3 Marks]
Ans: 
Here radius (r) = 21 cm
5ector angle (θ) = 120°
∴ Area cleaned by each sweep of the blades
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles [∵ there are 2 blades]
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 22 x  7 x 3 x 2 cm2
= 924 cm2

Q2: Find the area of the segment shown in the given figure, if radius of the circle is 21 cm and ∠AOB = 120°. (Take π = 22/7)       [2019, 3 Marks]Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

Ans: Given. O is the centre of the circle of radius 21cm and AB is the chord that subtends an angle of 120° at the centre.Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesDraw OM ⊥ AB,
Area of the minor segment AMBP = Area of sector OAPB - Area of ΔAOB
Now, area of sector OAPB
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 462 cm2
Since, OM ⊥ AB.
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles[∵ Perpendicular from the centre to the chord bisects the angle subtended by the chord at the centre.]
In ΔAOM, sin60° = AM/AO, cos60° = OM/OA
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Area of ΔAOB =
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Hence, Required Area = Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 462 - 381.92= 80.08 cm

Q3: In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region.       [2019, 3 Marks]Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to CirclesAns: Radius (r) of circle = 7 cm
Area of shaded region =
 Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
= 77 cm2

The document Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

1. How to find the area of a circle if the radius is given?
Ans. To find the area of a circle when the radius is given, you can use the formula A = πr^2, where A is the area and r is the radius of the circle.
2. How to calculate the circumference of a circle if the diameter is known?
Ans. If the diameter of a circle is known, you can find the circumference using the formula C = πd, where C is the circumference and d is the diameter of the circle.
3. What is the relationship between the area and circumference of a circle?
Ans. The circumference of a circle is directly proportional to its diameter, while the area of a circle is directly proportional to the square of its radius.
4. How can the area of a sector of a circle be calculated?
Ans. To find the area of a sector of a circle, you can use the formula A = (θ/360) x πr^2, where A is the area of the sector, θ is the angle of the sector in degrees, and r is the radius of the circle.
5. How to find the length of an arc in a circle?
Ans. The length of an arc in a circle can be calculated using the formula L = (θ/360) x 2πr, where L is the length of the arc, θ is the angle of the arc in degrees, and r is the radius of the circle.
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