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Please refer to MCQ Questions Chapter 11 Areas related to Circles Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 11 Areas related to Circles in Class 10 Mathematics provided below to get more marks in exams.

**Chapter 11 Areas related to Circles MCQ Questions**

Please refer to the following **Chapter 11 Areas related to Circles MCQ Questions Class 10 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 11 Areas related to Circles Class 10 Mathematics**

**Question. The outer and inner diameters of a circular ring are 34 cm and 32 cm respectively. The area of the ring is: **

(a) 66π cm^{2}

(b) 60π cm^{2}

(c) 33π cm^{2}

(d) 29π cm^{2}

**Answer**

C

**Question. In the figure, the area of the shaded portion is: **

(a) 15.25 cm^{2}

(b) 12.75 cm^{2}

(c) 18.05 cm^{2}

(d) 20.60 cm^{2}

**Answer**

A

**Question. If the sum of the areas of two circles with radii R _{1} and R_{2} is equal to the area of a circle of radius R, then:**

(a) R

_{1}+ R

_{2}= R

(b) R

_{1}

^{ 2}+ R

_{2}

^{2}= R

_{2}

(c) R

_{1}+ R

_{2}< R

(d) R

_{1}

^{ 2}+ R

_{2}

^{ 2}< R

_{2}

**Answer**

B

**Question. It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be: **

(a) 10 m

(b) 15 m

(c) 20 m

(d) 24 m

**Answer**

A

**Question. The radii of two concentric circles are 4 cm and 5 cm. The difference in the areas of these two circles is: **

(a) π

(b) 7 π

(c) 9 π

(d) 13 π

**Answer**

C

**Question. If the perimeter of a semi-circular protractor is 36 cm, then its diameter is: **

(a) 12 cm

(b) 13 cm

(c) 14 cm

(d) 15 cm

**Answer**

C

**Question. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then: **

(a) R_{1} + R_{2} = R

(b) R_{1} + R_{2} > R

(c) R_{1} + R_{2} < R

(d) Nothing definite can be said about the relation among R_{1} R_{2} and R.

**Answer**

A

**Question. The perimeter of a quadrant of a circle of radius ‘r’ is **

(a) π r/2

(b) 2πr

(c) r/ 2 [π + 4]

(d) 2πr + r/ 2

**Answer**

C

**Question. A wheel has diameter 84cm.The number of complete revolution it will take to cover 792m is. **

(a) 100

(b) 150

(c) 200

(d) 300

**Answer**

D

**Question. The area of the square that can be inscribed in a circle of radius 8cm is **

(a) 256cm^{2}

(b) 128cm^{2}

(c) 64√2cm^{2}

(d) 64cm^{2}

**Answer**

B

**Question. The area of a circle whose circumference π cm is **

(a) 11/2cm^{2}

(b) π/4cm^{2}

(c) π/2cm^{2}

(d) None of these

**Answer**

B

**Question. If the perimeter of a circle is equal to that of square, then the ratio of their areas is **

(a) 22/7

(b) 14/11

(b) 7/22

(d) 11/14

**Answer**

B

**Question. The length of an arc of a circle with radius 12cm is10 π cm. The central angle of this arc is. **

(a) 1200

(b) 60

(c) 750

(d) 1500

**Answer**

D

**Question. Area of sector of a circle of radius 36cm is 54 πcm ^{2.}Find the length of the corresponding arc of the circle is **

(a) 6π cm

(b) 3π cm

(c) 5π cm

(d) 8π cm

**Answer**

B

**Question. If the area of a circle is 154 cm ^{2}, then its circumference is: **

(a) 11 cm

(b) 22 cm

(c) 44 cm

(d) 55 cm

**Answer**

C

**Question. The area of a circle that can be inscribed in a square of side 6 cm is: **

(a) 36 p cm^{2}

(b) 18 p cm^{2}

(c) 12 p cm^{2}

(d) 9 p cm^{2}

**Answer**

D

**Question. A wire is in the shape of a circle of radius 21 cm. It is bent to form a square. The side of the square is: π = 22 /7 **

(a) 22 cm

(b) 33 cm

(c) 44 cm

(d) 66 cm

**Answer**

B

**Question. The area of a circle, whose circumference is 22 cm, is: **

(a) 54 cm^{2}

(b) 46 cm^{2}

(c) 40.5 cm^{2}

(d) 38.5 cm^{2}

**Answer**

D

**Question. If a circular grass lawn of 35 m in radius has a path 7 m wide running around it on the outside, then the area of the path is **

(a) 1450 m^{2}

(b) 1576 m^{2}

(c) 1694 m^{2}

(d) 3368 m^{2}

**Answer**

C

**Question. If a square ABCD is inscribed in a circle of radius ‘r’ and AB = 4 cm, then the value of r is: **

(a) 2 cm

(b) 2 √2 cm

(c) 4 cm

(d) 4 √2 cm

**Answer**

B

**Question. The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is: **

(a) 31 cm

(b) 25 cm

(c) 62 cm

(d) 50 cm

**Answer**

D

**Fill in the Blanks :**

**Question. If the circumference of a circle is 66 cm, then is its area is …………………. .**

**Answer**

**86.625 cm ^{2}**

**Question. If the area of a semi-circlular region is 308 sq cm, then its perimeter is ……………………. **

**Answer**

**72 cm**

**Question. The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km is …………………. **

**Answer**

**7000**

**Question. The area of the circle inscribed in a square of side a cm is …………………. . **

**Answer**

**πa ^{2}/4 cm^{2} **

**Question. The ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal is ………………….**

**Answer**

**π/√3**

**Question. If the area of circle is 616 cm ^{2}, then its circumference is …………………. . **

**Answer**

**88 cm**

**Question. Number of rounds that a wheel of diameter 7/ 11 metre will make in moving a distance of 2 km is ………. **

**Answer**

**1000 rounds**

**Question. If circumference and the area of a circle are numerically equal, then the diameter of the circle is …………………. . **

**Answer**

**4 units**

**(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.****(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.****(c) If Assertion is correct but Reason is incorrect.****(d) If Assertion is incorrect but Reason is correct.**

**Question. Assertion : If the outer and inner diameter of a circular path is 10m and 6m, then area of the path is 16π m ^{2 }.**

**Reason : If R and r be the radius of outer and inner circular path respectively then area of path = π (R**

^{2}– r^{2}).**Answer**

A

**Question. Assertion : If a wire of length 22 cm is bent in the shape of a circle, then area of the circle so formed is 40 cm ^{2}. **

**Reason : Circumference of the circle = length of the wire.**

**Answer**

D

**Question. Assertion : If the circumference of a circle is 176 cm, then its radius is 28 cm. ****Reason : Circumference = 2π × radius.**

**Answer**

A

**One Word Questions :**

**Question. In the figure, a shaded portion is cut off. Find the area of the remaining portion. (Π = 22/7) **

**Answer**

77cm^{2}

**Question. The numerical difference between circumference and diameter is 30cm. What is radius of the circles (Π = 22/7) **

**Answer**

7cm

**Question. The minute hand of a clock is √12cm long. What is the area described by the minute hand between 8:00am to 8:05am?**

**Answer**

cm²

**Question. What is the area of the shaded portion in the figure? **

**Answer**

18πcm²

**Question. In the figure find the area of the sector. **

**Answer**

3πcm²

**Question. ABCD is square kite of side 4cm. What is the area of the shaded portion? **

**Answer**

(16 – 4π)cm²

**Question. Find the perimeter of the shaded portion. **

**Answer**

42

**Question. Find the circumference of the circle with centre O.**

**Answer**

25 cm

**Question. Chord AB subtends an angle of 900 at the centre o. Find the area of the minor segment ACBA if radius OB=5cm. **

**Answer**

¯4. 1/2 25cm^{2}

**Question. The radius of two circles are in the ratio 3 : 4 and sum of the areas of two circle is equal to the area of third circle. What is the radius of third circle?**

**Answer**

5

**Question. What is the perimeter of the given plot? **

**Answer**

144cm

**Question. The archery target has three concentric circular regions. The diameter of the regions are in the 1 : 2 : 3. What is the ratio of their areas?**

**Answer**

1 : 4 : 9

**Question. Two circles having circumference C _{1} & C_{2} having radius R_{1} & R_{2} respectively. The circumference C of the third circle of radius R is such that C = C_{1} + C_{2} then what is R_{1} + R_{2} equal to?**

**Answer**

R

**Question. In the figure ABCD and EFGH are the square of sides 6cm and 1cm respectively. Find the area of the shaded region. **

**Answer**

(35 – π)cm²

**Question. If an arc forms an angle of 900 at the centre of the circle then what is the ratio of its length to the circumference of the circle?**

**Answer**

1 : 4

**Question. In the figure, What is the area of the blue ring? **

**Answer**

5 r^{2}

**Question. In the figure ABCD is the square of side 5cm. What is the area of the shaded region? **

**Answer**

(25 4 )cm^{2}

**Question. What is the area of the largest triangle that can be inscribed in a semicircle of radius r cm?**

**Answer**

r^{2}

**Question. Find the area of circle whose diameter is ‘d’.**

**Answer**

4¯d^{2}

**Question. What is the area of a sector of a circle of radius r and central angle θ ?**

**Answer**

¯360 r^{2}

**Question. A piece of wire 20cm long is bent into an arc of a circle subtending an angle of 600 at the centre then whtat is the radius of the circle?**

**Answer**

60 _cm

**Question. The radius of two circles are 13cm and 6cm respectively. What is the radius of the circle which has circumference equal to the sum of the circumference of two circles?**

**Answer**

19cm

**Question. The radius of circle is 3.5cm. What is the perimeter of the semicircle? (Π = 22/7)**

**Answer**

18cm.

**Question. Find the perimeter of the protactor if its diameter is 14cm. (Π = 22/7)**

**Answer**

36cm

**Question. The cost of fencing a circular field at the rate of Rs. 10 per meter is Rs. 440. What is the radius of the circular field? (Π = 22/7)**

**Answer**

7m

**Question. If an arc form an angle of 720 at the centre of the circle. Find the ratio of its length to its circumference.**

**Answer**

1 : 5

**Question. A paper is in the form of a square of side 20cm. Semicircle are down inside the square paper on two sides as diameter. The semicircular portions are cut off. Find the remaining** **paper. (Π = 3.14) **

**Answer**

86cm^{2}

**Question. If the circumference and area of a circle are numerically equal then what is the radius of the circle equal to?**

**Answer**

2 units

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