CBSE Class 10 Mathematics Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers. MCQ Class 10 Maths Areas Related to Circles with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Mathematics Areas Related to Circles MCQs with Answers to know their preparation level.
Multiple Choice Questions - Set - 1
Question 1:
Area of a sector of angle p (in degrees) of a circle with radius R is
(a) p/180 × 2πR
(b) p/180 × π R2
(c) p/360 × 2πR
(d) p/720 × 2πR2
Correct Answer – (D)
The area of a sector = (θ/360°) × π r2
Given, θ = p
So, area of sector = p/360 × π R2
Multiplying and dividing by 2 simultaneously,
= [(p/360)/(π R2)]×[2/2]
= (p/720) × 2πR2
Question 2 :
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is;
(a) 20cm
(b) 21cm
(c) 22cm
(d) 25cm
Correct Answer – (C)
Length of an arc = (θ/360°) × (2πr)
∴ Length of an arc AB = (60°/360°) × 2 × 22/7 × 21
= (1/6) × 2 × (22/7) × 21
Or Arc AB Length = 22cm
Question 3 :
The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm2
(b) 128 cm2
(c) 642 cm2
(d) 64 cm2
Correct Answer – (A)
Radius of circle = 8 cm
Diameter of circle = 16 cm = diagonal of the square
Let “a” be the triangle side, and the hypotenuse is 16 cm
Using Pythagoras theorem, we can write
162= a2+a2
256 = 2a2
a2= 256/2
a2= 128 = area of a square.
Question 4 :
If the perimeter of the circle and square are equal, then the ratio of their areas will be equal to:
(a) 14:11
(b) 22:7
(c) 7:22
(c) 11:14
Correct Answer – (A)
The perimeter of circle = perimeter of the square
2πr = 4a
a=πr/2
Area of square = a2 = (πr/2)2
Acircle/Asquare = πr2/(πr/2)2
= 14/11
Question 5 :
Area of the circle with radius 5cm is equal to:
(a) 60 sq.cm
(b) 75.5 sq.cm
(c) 78.5 sq.cm
(d) 10.5 sq.cm
Correct Answer – (C)
Radius = 5cm
Area = πr2 = 3.14 x 5 x 5 = 78.5 sq.cm
Question 6 :
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The area of the sector formed by the arc is:
(a) 200 cm2
(b) 220 cm2
(c) 231 cm2
(d) 250 cm2
Correct Answer – (C)
The angle subtended by the arc = 60°
So, area of the sector = (60°/360°) × π r2 cm2
= (441/6) × (22/7) cm2
= 231 cm2
Question 7 :
The area of a sector of a circle with radius 6 cm if the angle of the sector is 60°.
(a) 142/7
(b) 152/7
(c) 132/7
(d) 122/7
Correct Answer – (C)
Angle of the sector is 60°
Area of sector = (θ/360°) × π r2
∴ Area of the sector with angle 60° = (60°/360°) × π r2 cm2
= (36/6) π cm2
= 6 × (22/7) cm2
= 132/7 cm2
Question 8 :
The area of the circle that can be inscribed in a square of side 8 cm is
(a) 36 π cm2
(b) 16 π cm2
(c) 12 π cm2
(d) 9 π cm2
Correct Answer – (B)
Side of square = 8 cm
Diameter of a circle = side of square = 8 cm
Therefore, Radius of circle = 4 cm
Area of circle
= π(4)2
= π (4)2
= 16π cm2
Question 9 :
The largest triangle inscribed in a semi-circle of radius r, then the area of that triangle is;
(a) r2
(b) 1/2r2
(c) 2r2
(d) √2r2
Correct Answer – (A)
The height of the largest triangle inscribed will be equal to the radius of the semi-circle and base will be equal to the diameter of the semi-circle.
Area of triangle = ½ x base x height
= ½ x 2r x r
= r2
Question 10 :
The perimeter of a circle having radius 5cm is equal to:
(a) 30 cm
(b) 3.14 cm
(c) 31.4 cm
(d) 40 cm
Correct Answer – (C)
The perimeter of the circle is equal to the circumference of the circle.
Circumference = 2πr
= 2 x 3.14 x 5
= 31.4 cm
