Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Short Answer Questions: Areas Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Q1: In a circular table cover of radius 70 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the figure. Find the total area of the design.

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol: ∵ Radius of the circle = 70 cm and O is the centre of the circle.
∴ OA = OB = OC
Since ∆ABC is an equilateral triangle,
∴∠ABO = ∠BOC= ∠CDA = 120°
Draw OD⊥BC
Now in right ΔBDO,

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Area of equilateral ΔABC =  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Also, area of the circle = πr2  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

= 22 × 10 × 70 cm2 = 15400 cm2

Area of the shaded region= Area of Circle-Area of equilateral ΔABC
= 15400 cm2 − (3675√3) cm
= 15400 cm2 − (3675 × 1.73) cm2
= 15400 cm2 − 6357.75 cm2 = 9042.25 cm2.

Q2: Calculate the area other than the area common between two quadrants of the circles of radius 16 cm each, which is shown as the shaded region in the figure.

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol: 

Area of sector ADB

Class 10 Maths Chapter 11 Question Answers - Area Related to CirclesClass 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Area of the shaded region-I =  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Similarly,  area of the shaded region-II 384/7 cm2

∴ Total area of the shaded region = [Area of shaded region-I] + [Area of shaded region-II]

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Q3: In the figure, PQ = 24 cm, PR = 7 cm and O is the centre of the circle. Find the area of shaded region. (Take π = 3.14)

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol: In right Δ RPQ,
PR2 + PQ2 = RQ2
⇒ 72 + 242 = RQ2
⇒ 49 + 576 = RQ2
⇒ 625 = RQ2

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

⇒ Radius of semi-circle = 25/2 cm

∴ Area of semi-circle RQP

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Area of the shaded region=Area of semi-circle RQP − ar (right Δ RPQ)
=245.31 cm2 = 84 cm2 = 161.31 cm2.

Q4: The area of an equilateral triangle is 49√3. Taking each angular point as centre, circles are drawn with radius equal to half length of the side of the triangle. Find the area of triangle not included in the circles. [Take √3 = 1.73]

Sol: Let the given equilateral triangle be ABC, such that its side = 14 cm.

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Since each angle of an equilateral triangle = 60°,
∴ Area of a sector having θ as 60° and radius 14/2 i.e. 7 cm.

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

⇒ Area of 3 sectors  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

= 77 cm2
∴ Area of the shaded region = [Area of equilateral ∆ ABC] − [Area of 3 sectors]
= 84.77 cm2 − 77 cm2 = 7.77 cm2.

Q5: Four equal circles are described at the four corners of the square so that each touches two of the others, the shaded area enclosed between the circles is 22/7 cm2 Find the radius of each circle.

Sol: Let 'r' cm be the radius of each circle.
∴ side of the square = 2r
Now, area of shaded region

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

But the area of shaded region  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

But r cannot be − ve, so r = 2 cm

Q6: A square OABC is inscribed in a quadrant OABQ of a circle as shown in the figure. If OA = 14 cm, find the area of the shaded region. [use π = 22/7]

Sol: OABC is a square with side = 14 cm.
∴ Area of the square OABC = 14 cm × 14 cm = 196 cm2

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Now, the diagonal of the square OABC 
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles
⇒ Radius of the quadrant OPBQ
  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles
∴ Area of the quadrant OABQ

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Area of the shaded region
= 308 cm2 − 196 cm2 = 112 cm2.

Q7: In the figure, ABDC is a quadrant of a circle of radius 14 cm and a semi-circle is drawn with diameter BC. Find the area of the shaded region.

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol: We have, in the right Δ ABC,

BC2 = AB2 + AC2 = 142 + 142 = 2 (14)2

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Radius of the semi-circle =  Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Area of semi-circle BEC

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Area of the quadrant with radius 14 cm,

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

= 98 cm2

Area of the shaded region Class 10 Maths Chapter 11 Question Answers - Area Related to CirclesClass 10 Maths Chapter 11 Question Answers - Area Related to Circles

= 154 cm2 + 98 cm2 − 154 cm2 = 98 cm2.

Q8: In the figure, find the perimeter of the shaded region where, ADC, AEB and BFC are semicircles on diameters AC, AB and BC respectively.

Sol: Diameter of semi-circle ADC

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

= 2.1 cm
∴ Circumference of semi-circle ADC

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Diameter of semi-circle AEB = 2.8 cm
⇒ Radius of semi-circle

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Circumference of semi-circle

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Diameter of semi-circle BFC = 1.4 cm
⇒ Radius of semi-circle BFC = 0.7 cm
∴ Circumference of semi-circle BFC

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

∴ Total perimeter of the shaded region = 6.6 cm + 4.4 cm + 2.2 cm = 13.2 cm.

Q9: In the figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region.

[use π = 3.14]

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol. ∵ ΔABC is an equilateral triangle.
∴∠A = ∠B = ∠C = 60°
Area of sector AFEA
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Area of all the three sectors

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Thus, area of the shaded region = 39.25 cm2.

Q10: In figure OABC is a quadrant of a circle of radius 7 cm. If OD = 4 cm, find the area of the shaded region. [Use π = 22/7]

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Sol: We have, the centre of the circle as ‘O’ and radius (r) = 7 cm

Area of the quadrant OABC Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

=  7 × 2 = 14 cm2
∴ Area of the shaded region = (Area of the quadrant OABC) – (Area of ∆COD)
Class 10 Maths Chapter 11 Question Answers - Area Related to Circles

The document Class 10 Maths Chapter 11 Question Answers - Area 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 Question Answers - Area Related to Circles

1. What is the formula to find the area of a circle?
Ans. The formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.
2. How is the circumference of a circle related to its radius?
Ans. The circumference of a circle is directly proportional to its radius. The formula to find the circumference is C = 2πr, where C represents the circumference and r represents the radius.
3. Can the area of a circle be negative?
Ans. No, the area of a circle cannot be negative. The area represents the space enclosed within the circle, and it is always a positive value.
4. How can the radius of a circle be calculated if the area is given?
Ans. If the area of a circle is given, the radius can be calculated using the formula r = √(A/π), where r represents the radius and A represents the area.
5. What is the value of pi (π) and why is it used in the formulas for a circle?
Ans. The value of pi (π) is approximately 3.14159. It is a mathematical constant that represents the ratio of a circle's circumference to its diameter. Pi is used in the formulas for a circle to calculate its area and circumference accurately.
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