Please refer to the **MCQ Questions for Class 10 Maths Areas related to Circles **with Answers. The following Areas related to Circles Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Areas related to Circles Class 10 MCQ Questions with Answers

Please see below Areas related to Circles Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. O is the centre of a circle of diameter 4 cm and OABC is a square, if the shaded area is 1/3 area of the square, then the side of the square is ________.**

(A) π √3 cm

(B) 3 √π cm

(C) 3 √π cm

(D) 3 π cm

## Ans.

B

**Question.** A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. [use π = 22/7]

(A) 44 cm^{2}

(B) 308 cm^{2}

(C) 77 cm^{2}

(D) 154 cm^{2}

## Ans.

D

**Question.****If the difference between the area of a regular hexagonal plot and the area of a circular swimming tank circumscribed in it is 26.705 m ^{2}. Find the radius of the circular swimming tank. (p = 3.143, 3 = 1.732)**

(A) 4 cm

(B) 7 cm

(C) 11 cm

(D) 9 cm

## Ans.

B

**Question.** The areas of two concentric circles are 962.5 cm^{2} and 1386 cm^{2} respectively. The width of the ring is ________.

(A) 3.4 cm

(B) 3.5 cm

(C) 3.2 cm

(D) 3.1 cm

## Ans.

B

**Question.****A chord of a circle subtends an angle of 60° at the centre. If the length of the chord is 100 cm, find the area of the major segment.**

(A) 30720.5 cm^{2}

(B) 31021.42 cm^{2}

(C) 30391.7 cm^{2}

(D) 30520.61 cm^{2}

## Ans.

D

**Question.** Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.

(A) 1125 cm^{2}

(B) 1321 cm^{2}

(C) 1210 cm^{2}

(D) 1225 cm^{2}

## Ans.

C

**Question.** The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. The area of the sector is ________.

(A) 15.1 cm^{2}

(B) 15.5 cm^{2}

(C) 15.6 cm^{2}

(D) 15.9 cm^{2}

## Ans.

C

** Question. Circle C_{1} passes through the centre of circle C_{2} and is tangential to it. If the area of C_{1} is 4 cm^{2}, then the area of C_{2} is ________.**(A) 8 cm

^{2}

(B) 8 2 √π cm

(C) 16 cm

^{2}

(D) 16 2 √π cm

## Ans.

C

**Question.** In the given figure, the area of the shaded region is _____.

(A) 3π cm^{2}

(B) 6π cm^{2}

(C) 9π cm^{2}

(D) 7π cm^{2}

## Ans.

A

**Question.** The ratio of the outer and inner perimeters of a circular path is 23 : 22. If the path is 5 metres wide, the diameter of the inner circle is

(A) 55 m

(B) 110 m

(C) 220 m

(D) 230 m

## Ans.

C

**Question.****An oval shaped meeting table made of wood has its dimensions as shown in figure. Find the cost of polishing it at ₹ 3.50 per sq. m. (Use p = 3.14)**

(A) ₹ 310.75

(B) ₹ 308.91

(C) ₹ 250.25

(D) ₹ 360.82

## Ans.

B

**Question.****The diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 km per hour?**

(A) 200

(B) 210

(C) 250

(D) 240

## Ans.

C

**Question.****A square water tank has its sides equal to 40 m. There are four semicircular grassy plots all round it. Find the cost of turfing** **the plots at ₹ 1.25 per sq. m.**

(A) ₹ 2671

(B) ₹ 4401

(C) ₹ 2512

(D) ₹ 3140

## Ans.

D

**Question.** A man runs around a circle of radius 50 m at a speed of 12 km/h. The time taken by him for going around it ten times is _____. (π = 3.14)

(A) 10 mins 42 secs

(B) 12 mins 35 secs

(C) 15 mins 42 secs

(D) 10 mins 35 secs

## Ans.

C

**Question.** A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per m^{2}.

(A) ₹ 31425

(B) ₹ 28260

(C) ₹ 352.40

(D) None of these

## Ans.

D

**Question.** In the given figure three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region in terms of p and √3.

## Ans.

D

**Question.** Match the shaded region given in Column-I with their areas in Column-II.

(A) (P) → (iii); (Q) → (ii); (R) → (i)

(B) (P) → (ii); (Q) → (i); (R) → (iii)

(C) (P) → (ii); (Q) → (iii); (R) → (i)

(D) (P) → (iii); (Q) → (i); (R) → (ii)

## Ans.

C

**Question.****The circumcircle of ΔABC with ∠A = 60° has its centre at O and radius equal to 2 cm. Circle centered at O _{1} touches the circumcircle and also OB and OC. The radius of the smaller circle is (in cm) __**.

(A)12-4√3

(B) 6-√3/2

(C) 3-√3/2

(D) 4√3-6

## Ans.

D

**Question.** In the given figure, ABC is a right-angled triangle, right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

(A) 7 sq. units

(B) 8 sq. units

(C) 5 sq. units

(D) 6 sq. units

## Ans.

D

**Question.** In the given figure, ABCD is a square of side 10 cm. Find

(i) Area of inscribed circle

(ii) Area of circumscribed circle

(iii) Area of shaded region

## Ans.

B

**Question.****What is The area of a sector of a circle of radius 16 cm cut off by an arc which is 18.5 cm long?**

(a) 168cm^{2}

(b) 148cm^{2}

(c) 154cm^{2}

(d) 176cm^{2}

## Ans.

B

**Question.** The given figure is made up of a rectangle**and 2 identical circles. Given that the length** **of the rectangle is 28 cm.**

What is the area of the shaded region? (Use π = 22/7.)

(a) 119 cm^{2}

(b) 105 cm^{2}

(c) 152 cm^{2}

(d) 123 cm^{2}

## Ans.

A

**Question.** The diameters of the wheels of a car are each 63 cm. Find the distance travelled by the car when the wheels make 1000 revolutions.

(a) 1890 m

(b) 1980 m

(c) 1900 m

(d) 1800 m

## Ans.

B

**Question.** The circumference of a circle exceeds its**diameter by 30 cm. Find the radius of the** **circle.**

(a) 7 cm

(b) 14 cm

(c) 21 cm

(d) 28 cm

## Ans.

A

**Question.** If the circumference of a circle is increased**by 50%, by what percent will its area be** **increased?**

(a) 75%

(b) 100%

(c) 125%

(d) 150%

## Ans.

C

**Question.****The figure given is made up of a square with a circle inscribed in it.**

What is the area of the shaded region? (Take π = 3.14 .)

(a) 6.28 cm^{2}

(b) 1.42 cm^{2}

(c) 4.91 cm^{2}

(d) 7.36 cm^{2}

## Ans.

A

**Question.** By The shaded part of the given figure shows a running track in a stadium.

Find the area of the track. (Take π = 22/7 .)

(a) 2058m^{2}

(b) 1546m^{2}

(c) 3514m^{2}

(d) 1923m^{2}

## Ans.

A

**Question.** A bucket is pulled from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/s, find the number of complete evolutions that the wheel makes in raising the bucket. (Take π = 22/7.)

(a) 10

(b) 55

(c) 25

(d) 40

## Ans.

D

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

(a) 2r cm^{2}

(b) r2 cm2

(c) 2r2 cm^{2}

(d) r/2 cm^{2}

## Ans.

B

**Question.** How many plants will be there in a circular bed whose outer edge measures 30 cm allowing 4 cm2 for each plant?

(a) 18

(b) 750

(d) 24

(d) 120

## Ans.

A

**Question. When the circumference and area of a circle are numerically equal, find the numerical value of its diameter.**

(a) π/2

(b) 8

(c) 2π

(d) 4

## Ans.

D

**Question. If the area of circle is numerically equal to twice its circumference, then the diameter of the circle is **

(a) 4 units

(b) 6 units

(c) 8 units

(d) 12 units

**Answer**

C

**Question. The angle described by a minute hand in 5 minutes is **

(a) 30°

(b) 60°

(c) 90°

(d) None of these

**Answer**

A

**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

**Question. In a circle of diameter 42 cm,if an arc subtends an angle of 60° at the centre where π = 22/7 , then what will be the length of arc ? **

(a) 11 cm

(b) 20 cm

(c) 22 cm

(d) 28 cm

**Answer**

C

**Question. What is the area of the circle that can be inscribed in a square of side 6 cm? **

(a) 9 π cm^{2}

(b) 11 π cm^{2}

(c) 16 π cm^{2}

(d) 15 π cm^{2}

**Answer**

A

**Question. The area of a quadrant of a circle whose circumference is 25 cm is **

(a) 24 cm^{2}

(b) 28 cm^{2}

(c) 32.5 cm^{2}

(d) 38.5 cm^{2}

**Answer**

D

**Question. The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences? **

(a) 1 : 2

(b) 2 : 1

(c) 3 : 2

(d) 2 : 3

**Answer**

C

**Question. The cost of fencing a circular field at the rate of ` 24 per metre is ` 5280. The radius of the field is **

(a) 15 m

(b) 35 m

(c) 25 m

(d) 30 m

**Answer**

B

**Question. The radii of two circles are 8 cm and 6 cm respectively. The radius of the circle having area equal to the sum of the areas of the two circles is **

(a) 5 cm

(b) 10 cm

(c) 12 cm

(d) 15 cm

**Answer**

B

**Question. The perimeter (in cm) of a square circumscribing a circle of radius a cm is **

(a) 2a

(b) 4a

(c) 6a

(d) 8a

**Answer**

D

**Question. What is 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? **

(a) 20 cm

(b) 30 cm

(c) 50 cm

(d) 80 cm

**Answer**

C

**Question. An athlete runs on a circular track of radius 49 m and covers a distance of 3080 m along its boundary. How many rounds has he taken to cover this distance? [Take π =22/7] **

(a) 5

(b) 8

(c) 10

(d) 15

**Answer**

C

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

(a) 22 : 7

(b) 14 : 11

(c) 7 : 22

(d) 11 : 14

**Answer**

B

**Question. A road which is 7 m wide surrounds a circular park whose circumference is 88 m. The area of the road is **

(a) 220 m^{2}

(b) 340 m^{2}

(c) 550 m^{2}

(d) 770 m^{2}

**Answer**

D

**Question. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. The length of the arc is **

(a) 11 cm

(b) 22 cm

(c) 27 cm

(d) 44 cm

**Answer**

B

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

(a) 256 cm^{2}

(b) 128 cm^{2}

(c) 64 2 2 cm

(d) 64 cm^{2}

**Answer**

B

**Question. The area of the largest triangle that can be inscribed in a semi-circle of radius r units will be **

(a) r sq. units

(b) r/2 sq. units

(c) r^{2} sq. units

(d) 2r sq. units

**Answer**

C

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

(a) 32 2 cm^{2}

(b) 45 2 cm^{2}

(c) 55 2 cm^{2}

(d) 77 2 cm^{2}

**Answer**

D

**Question. An arc of length 15.7 cm subtends a right angle at the centre of the circle. Then the radius of the circle is **

(a) 20 cm

(b) 10 cm

(c) 15 cm

(d) 12 cm

**Answer**

B