# MCQ Questions for Class 10 Maths Areas Related to Circles with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 12 Areas Related to Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Areas Related to Circles MCQs with Answers to know their preparation level.

## Class 10 Maths MCQs Chapter 12 Areas Related to Circles

Circle Multiple Choice Question 1. The area of the circle is 154 cm2. The radius of the circle is
(a) 7 cm
(b) 14 cm
(c) 3.5 cm
d) 17.5 cm

Areas Related To Circles Class 10 MCQ With Answer: dExplaination: Reason: Area of circle = 154 cm²
⇒ nr² = 154 cm2
⇒ $$\frac{22}{7}$$ × r² = 154
⇒ r² = 154 × $$\frac{22}{7}$$
⇒ r² = 7 × 7 = 49
∴ r = √49 = 7

2. If angle of sector is 60°, radius is 3.5 cm then length of the arc is
(a) 3 cm
(b) 3.5 cm
(c) 3.66 cm
(d) 3.8 cm

Explaination: Reason: Here r = 3.5 cm = $$\frac{35}{10}$$ = $$\frac{7}{2}$$ cm θ = 60°
Length of arc = $$\frac{θ}{360}$$ × 2πr = $$\frac{60}{360}$$ × 2 × $$\frac{22}{7}$$ = × $$\frac{7}{2}$$ × $$\frac{1}{6}$$ × 22 = $$\frac{11}{6\3}$$ = 3.66 cm

Areas Related To Circles MCQs Question 3. The area of a quadrant of a circle whose circumference is 22 cm, is Explaination: Reason: Here 2πr = 22 cm
2 × $$\frac{22}{7}$$ × r = 22
⇒ r = 22 × $$\frac{7}{22}$$ × $$\frac{1}{2}$$ = $$\frac{7}{2}$$ cm
∴ Area of quadrant of circle = $$\frac{1}{4}$$πr² = $$\frac{1}{4}$$ × $$\frac{22}{7}$$ × $$\frac{7}{2}$$ × $$\frac{7}{2}$$ = $$\frac{77}{8}$$ cm²

4. If 0 is the angle in degrees of a sector of a circle of radius V, then area of the sector is 5. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 7 m long rope. The area of that part of the field in which the horse can graze, is
(a) 77 cm²
(b) $$\frac{77}{2}$$ cm²
(c) 154 cm²
(d) $$\frac{77}{4}$$ cm²

MCQ on Areas Related To Circles With Answer: b
Explaination:  6. The area of the circle whose diameter is 21 cm is
(a) 346.5 cm²
(b) 37.68 cm²
(c) 18.84 cm²
(d) 19.84 cm²

Explaination: Reason: Here diameter = 21 cm
∴ Radius r = $$\frac{21}{2}$$ cm
Area of the circle, A = πr²
∴ $$A=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}=11 \times 3 \times \frac{21}{2}=\frac{693}{2}=346.5 \mathrm{cm}^{2}$$

7. The area of the sector of a circle with radius 6 cm and of angle 60° is
(a) 9.42 cm²
(b) 37.68 cm²
(c) 18.84 cm²
(d) 19.84 cm²

Explaination: Reason: Here r = 6 cm, θ = 60°
Area of the sector = $$\frac{θ}{360}$$
∴ Area = $$\frac{60}{360}$$ × 3.14 × 6 × 6 = $$\frac{1}{6}$$ × 3.14 × 6 × 6 = 3.14 × 6 = 18.84 cm²

8. The area of a circle whose circumference is 22 cm, is
(a) 11 cm²
(b) 38.5 cm²
(c) 22 cm²
(d) 77 cm²

Explaination: 9. The area of a circle is 154 cm2. Its diameter is
(a) 7 cm
(b) 14 cm
(c) 21 cm
(d) 28 cm

Explaination: Reason: Here area of the circle, A = 154 cm², Radius, r = ?
Area of the circle = 154 cm² …(Given)
∴ πr² = 154
⇒ $$\frac{22}{7}$$ × r² = 154
⇒ r² = 154 × latex]\frac{7}{22}[/latex] = 7 × 7
⇒ r = 7 cm
∴ Diameter of the circle = 2 × r = 2 × 7 = 14 cm

10. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is
(a) 153.9 cm²
(b) 102.6 cm²
(c) 51.3 cm²
(d) 205.2 cm²

Explaination: Reason: Angle swept by the minute hand in 1 minute = (360° ÷ 60) = 6°
∴ θ = 30°
∴ Angle swept by the minute hand in 5 minutes = 6° × 5 = 30°
Length of minute hand (r) = 14 cm
∴ Area swept = $$\frac{θ}{360}$$πr² = $$\frac{30}{360}$$ × $$\frac{22}{7}$$ × 14 × 14 = $$\frac{154}{3}$$ = 51.3 cm²

MCQ Questions For Class 10 Maths Areas Related To Circles Question 11. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle which has circumference equal to the sum of the circumference of two circles is
(a) 35 cm
(b) 10 cm
(c) 21 cm
(d) 28 cm

Explaination: Reason: Let the radii of two circles be r1 and r2 and the radius of large circle be r.
∴ r1 = 19 cm, r2 = 9 cm
Circumference of two circles = C1+ C2 …(where C = circle)
= 2πr1 + 2πr2 = 2π × 19 + 2π × 9 = 38π + 18π = 56π
∴ Circumference of large circle = 56π
⇒ 2πr = 56π
⇒ r = 28
∴ Radius of large circle = 28 cm

12. The area of the circle that can be inscribed in a square of side 6 cm, is
(a) 18π cm²
(b) 12π cm²
(c) 9π cm²
(d) 14π cm²

Explaination: Reason: Size of square = 6 cm, radius = $$\frac{6}{2}$$ = 3 cm;