Grade 10 Exam  >  Grade 10 Notes  >  Mathematics for Grade 10  >  Previous Year Questions: Areas Related to Circles - 2

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

Previous Year Questions 2017

Q10: A chord PQ of a circle of radius 10 cm subtends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle.    (Delhi 2017)

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

Ans:  Radius of the circle = 10 cm
Central angle subtended by chord AB = 60°
Area of minor sector OACB
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Area of equilateral triangle OAB formed by radii and chord
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
∴ Area of minor segment ACBD
= Area of sector OACB - Area of triangle OAB
= (52.38 - 43.30) cm2 = 9.08 cm2 
Area of circle = πr
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
∴ Area of major segment ADBE
= Area circle - Area of minor segment
= (314.28 - 9.08) cm2 = 305.20 cm2


Q11: In the given figure, ΔABC is a right-angled triangle in which ∠A is 90°. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.     (Al 2017)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: In right triangle ABC.
AB2 + AC2 = BC2
⇒ (3)2 + (4)2 = BC2 ⇒ 9 + 16 = BC2  ⇒ 25 = BC2 
∴ BC = 5 cm
Now, Area of shaded region = Area of semicircle on side AB + area of semicircle on side AC - area of semicircle on side BC + area of ΔABC
Now, Area o f semicircle on side AB 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
Hence area of the shaded region = 6 cm2


Q12: In Fig. 12.51, O is the centre of the circle with AC = 24 cm , AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region.   (CBSE (AI) 2017)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: In right angle triangle ABC
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 shaded region = area of semicircle - area of ΔCAB + area of quadrant BOD
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

Previous Year Questions 2016

Q13: In Fig. 12.34, O is the centre of a circle such that diameter AB =13 cm and AC = 12 cm. ISC is joined. Find the area of the shaded region. (Take k = 3.14)    (CBSE (AI) 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans:  In ΔABC, ∠ACB = 90° (Angle in the semicircle)
∴ BC2 + AC2 = AB2
∴ BC2 = AB2 -AC2
= 169 - 144 = 25
∴ BC = 5 cm
Area of the shaded region = area of semicircle - area of right AABC
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles


Q14: In Fig. 12.35, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre 0 and radius OP while arc PBQ is a semi-circle drawn on PQ as diameter with centre M.
If OP = PQ = 10 cm show that area of shaded region is 25 Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles    (CBSE (Delhi) 2016)

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

Ans: Since OP = PQ = QO
⇒ APOQ is an equilateral triangle
∴ ∠POQ = 60°
Area of segment PAQM
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 semicircle with M as centre Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
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


Q15: In figure, the boundary of shaded region consists of four semicircular arcs, two smallest being equal. If diameter of the largest is 14 cm and that of the smallest is 3.5 cm, calculate the area of the shaded region. Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles    (Foreign 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: Given AD = 14 cm, AB = CD = 3.5 cm
∴ BC = 7 cm
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Area of shaded region
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles


Q16: Find the area of the shaded region in Fig. 12.23, where a circular arc of radius 6 cm has been drawn with vertex 0 of an equilateral triangle ΔOAB of side 12 cm as centre.    (NCERT, CBSE (F) 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: We have, radius of circular region = 6 cm and each side of ΔOAB = 12 cm.
∴ Area of the circular portion
= area of circle - area of the sector
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Now, area of the equilateral triangle OAB
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
∴ Area of shaded region = area of circular portion + area of equilateral triangle OAB
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles


Q17: An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 12.46). From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length o f the belt that is still in contact with the pulley. Also find the shaded area.  (Use π = 3.14 and √3 = 1.73)    (CBSE Delhi 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles 

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

Ans: 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
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
PA = 5√S cm = BP (Tangents from an external point are equal)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Shaded area = 43 .25 - 26 .17 = 17.08 cm2


Q18: In Fig. 12.47, a sector OAP of a circle with centre O, containing angle 0. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles    (CBSE (AI) 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
In right ΔAOB
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Perimeter 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


Q19: Find the area of the shaded region in Fig. 12.48, where Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles are semicircles of diameter 14 cm, 3.5 cm, 7 cm and 3.5 cm respectively. Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles   (CBSE (E) 2016)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: 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


Previous Year Questions 2015

Q20:  In figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region.     (Foreign 2015)

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

Ans: Area of shaded region = area of trapezium - (area of 4 sectors)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
Total area of all sector
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
[Sum of angles of a quadrilateral is 360°]
From (i) and (ii),
Area of shaded region = 350 - 154 = 196 cm2


Q21: Find the area of the shaded region given in Fig.    (Delhi 2015)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles

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

Ans: Side of the square = 14 cm
Area of the square = a2 
= 142 - 196 cm2 
Let radius of a semicircle=x
radius of two semicircles = 2x
side of inner square = diameter of semicircle = 2x
According to figure 2x + 2x = 8
4x = 8 ⇒ x = 2 cm
⇒ Side of inner square = 4 cm
Area of unshaded region = area of inner square + 4 (Area of a semicircle)
Class 10 Maths Chapter 11 Previous Year Questions - Areas Related to Circles
∴ Area of shaded region = area of square - area of unshaded region
= (196-16-871) cm2 = (180-8π) cm2 
= 180-8 x 3.14 = 180-25.12 = 154.88 cm2

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

1. What is the formula to find the area of a sector of a circle?
Ans. The formula to find the area of a sector of a circle is (θ/360) * π * r^2, where θ is the central angle of the sector and r is the radius of the circle.
2. How can we find the length of an arc in a circle?
Ans. The formula to find the length of an arc in a circle is (θ/360) * 2 * π * r, where θ is the central angle of the sector and r is the radius of the circle.
3. How do we calculate the area of a circle when only the circumference is given?
Ans. If only the circumference of the circle is given, we can use the formula A = (C^2) / (4π), where A is the area of the circle and C is the circumference.
4. Can we find the area of a segment of a circle without knowing the angle?
Ans. Yes, we can find the area of a segment of a circle without knowing the angle by using the formula A = A_sector - A_triangle, where A_sector is the area of the sector and A_triangle is the area of the triangle formed by the radii of the circle and the chord of the segment.
5. How do we calculate the area of a circle inscribed in a triangle?
Ans. To calculate the area of a circle inscribed in a triangle, we can use the formula A = (r*s), where r is the radius of the circle and s is the semi-perimeter of the triangle.
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