# Areas related to Circles MCQ Class 10 Mathematics

Please refer to Chapter 11 Areas related to Circles MCQ Class 10 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 10 Mathematics. Students should refer to MCQ Questions for Class 10 Mathematics with Answers to score more marks in Grade 10 Mathematics exams. Students should read the chapter Areas related to Circles and then attempt the following objective questions.

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

The Areas related to Circles MCQ Class 10 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

**Question. The area of a circular path of uniform width b surrounding a circular region of radius r is **

(a) π (2r+b) r sq. units

(b) π (2r+b)b sq. units

(c) π (b+r) r sq. units

(d) π (b+r)b sq. units

**Answer**

B

**Question. Smita shaded a square cardboard, as shown below: **

**Which of these is closest to the area of the shaded region? **

(a) 364.52 cm^{2}

(b) 439.9 cm^{2}

(c) 492.4 cm^{2}

(d) 572.4 cm^{2}

**Answer**

A

**Question. The circumference of two circles are in the ratio 2 : 3. The ratio of their areas is **

(a) 2 : 3

(b) 4 : 9

(c) 9 : 4

(d) None of these

**Answer**

B

**Question. If the perimeter of a semicircular protractor is 36 cm; its diameter is **

(a) 14 cm

(b) 16 cm

(c) 18 cm

(d) 12 cm

**Answer**

A

**Question. 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. Area of the largest triangle that can be inscribed in a semi-circle of radius r units is **

(a) r^{2}sq. units

(b) 1/2 r^{2}sq. units

(c) 2r^{2}sq. units

(d) √2r^{2}sq. units

**Answer**

A

**Question. If the circumference of a circle and the perimeter of a square are equal, then **

(a) Area of the circle = Area of the square

(b) Area of the circle > Area of the square

(c) Area of the circle < Area of the square

(d) Nothing definite can be said about the relation between the areas of the circle and square.

**Answer**

B

**Question. The area of the shaded region in the given figure is (Take π = 3.14). **

(a) 75 cm^{2 }

(b) 73 cm^{2}

(c) 70 cm^{2}

(d) none of them

**Answer**

B

**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) None of these

**Answer**

A

**Question. The difference between the circumference and radius of a circle is 37 cm. The area of circle is **

(a) 111 cm^{2}

(b) 184 cm^{2}

(c) 154 cm^{2}

(d) 259 cm^{2}

**Answer**

C

**Question. On increasing the distance of circle by 40%, its area will be increased by **

(a) 40%

(b) 80%

(c) 96%

(d) none of them

**Answer**

C

**Question. A square ABCD is inscribed in a circle of radius ‘r’. The area of the square in square units is **

(a) 3r^{2}

(b) 2r^{2}

(c) 4r^{2}

(d) none of them

**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 area of the square is same as the area of circle. Then their perimeter are in the ratio **

(a) 1 : 1

(b) √π : 2

(c) 2:π

(d) none of them

**Answer**

B

**Question. A paper is in the form of a rectangle ABCD in which AB = 18 cm and BC = 14 cm. A semicircular portion with BC as diameter is cut off. The area of the remaining paper is **

(a) 175 cm^{2}

(b) 165 cm^{2}

(c) 145 cm^{2}

(d) none of them

**Answer**

A

**Question. The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. The area of sector is **

(a) 44 cm^{2}

(b) 44.6 cm^{2}

(c) 44.8 cm^{2}

(d) none of them

**Answer**

C

**Question. The given figure shows a plot of land, which is made up of 2 semicircles, a rectangle and an isosceles triangle. The diameter of the bigger semicircle is 7 m longer than that of the smaller semicircle. (Use π = 22/7). **

**If the shaded region is covered with grass, find the area of the land covered with grass.**(a) 502 m

^{2}

(b) 497 m

^{2}

(c) 433 m

^{2}

(d) 564 m

^{2}

**Answer**

B

**Question. Find the area of a segment of a circle of radius 21 cm if the angle made by the arc of the segment has a measure of 60° . **(a) 45.27 cm

^{2}

(b) 40.27 cm

^{2}

(c) 40.8 cm

^{2}

(d) 44.27 cm

^{2}

**Answer**

B

**Question. If the ratio of areas of two circles is 16:25, what is the respective ratio of their circumferences ? **

(a) 25:16

(b) 5:4

(c) 4:5

(d) 3:5

**Answer**

C

**Question. The figure given is made up of a circle and 3 identical semicircles. 0 is the centre of the circle and XY is the diameter of the circle. **

**Given that XY is 28 cm, find the perimeter of the shaded part of the figure. (Use π = 22/7)…..**

(a) 67 cm

(b) 50 cm

(c) 80 cm

(d) 15 cm

**Answer**

C

**Question. The top of a dining table is rectangular, 2x units long and x units wide, with two semicircles along the breadth. Find the area of the table. **

(a) π + 4x^{2} /4 sq units

(b) (π + 4)/4 , x^{2} sq units

(c) (π + 8/4) x^{2} sq units

(d) 2(π + 4)x^{2} sq.units

**Answer**

C

**Question. The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into four parts of equal area. Find the radius of one of the three concentric circles. **

(a) 8 √3cm

(b) 2 √3cm

(c) 10 √3cm

(d) 14 √3cm

**Answer**

C

**Question. The figure shows an isosceles triangle and a semicircle with centre O. **

**Given that the radius of the semicircle is 2.8 cm, find the perimeter of the given figure.**

(a) 15.6 cm

(b) 18.8 cm

(c) 16.8 cm

(d) 20.4 cm

**Answer**

B

**Question. A copper wire, when bent in the form of a square, encloses an area of 484 cm ^{2} . If the same wire is bent in the form of a circle, find the area in cm^{2} . **

(a) 606

(b) 661

(c) 616

(d) 610

**Answer**

C

**Question. If the length of the arc of a circle having a central angle 36° is 22 cm, what is the area of the circle? **

(a) 3580 cm^{2}

(b) 3850 cm^{2}

(c) 3058 cm^{2}

(d) 3805 cm^{2}

**Answer**

B

**Question. The figure shows a right-angled triangle and a semicircle. PQ is the diameter of the semicircle. **

**Find the perimeter of the whole figure.**

(a) 13+ 8π

(b) 30+5π

(c) 18+ 6π

(d) 18+10π

**Answer**

C

**Question. If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r then the relation between corresponding angles θ _{1} and θ_{2} is **

(a) θ1=2θ

_{2}

(b) θ1=θ

_{2}

(c) θ1=1/2θ

_{2}

(d) θ1=4θ

_{2}

**Answer**

A

**Question. A racetrack is in the form of a ring whose inner circumferences is 352 m and outer circumference is 396 m. The width of the track is **

(a) 4 m

(b) 6 m

(c) 8 m

(d) 7 m

**Answer**

D

**Question. A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. The area of major segment is **

(a) 210 cm^{2}

(b) 285.7 cm^{2}

(c) 185.5 cm^{2}

(d) 258.1 cm^{2}

**Answer**

B

**Question. The area of a sector of a circle with radius 14 cm and central angle 45° is **

(a) 76 cm^{2}

(b) 77 cm^{2}

(c) 66 cm^{2}

(d) 55 cm^{2}

**Answer**

B

**Question. If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is **

(a π r^{2}θ/ 360°

(b) π r^{2}θ/ 180°

(c) 2π rθ 360 °

(d) 2πrθ/180º

**Answer**

A

**Question. The area of the shaded region in fig, where arcs drawn with centres P, Q, R and S intersect in pairs at mid points A, B, C and D of the sides PQ, QR, RS and SP respectively of a square PQRS, is **

(a) 30.86 cm^{2}

(b) 30.86 m^{2}

(c) 30.86 mm^{2}

(d) 30.86 km^{2}

**Answer**

A

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

(a) 36 π cm^{2}

(b) 18 π cm^{2}

(c) 12 π cm^{2}

(d) 9 π cm^{2}

**Answer**

D

**Question. A wire can be bent in the form of a circle of radius 35 cm. If it is bent in the form of a square, then its area will be **

(a) 3025 cm^{2}

(b) 3025/2cm^{2}

(c) 1225 cm^{2}

(d) 2450 cm^{2}

**Answer**

A

**Question. A drain cover is made from a square metal of side 40 cm having 441 holes of diameter 1 cm each drilled in it. The area of remaining square plate is **

(a) 1250.5 cm^{2}

(b) 1256.5 cm^{2}

(c) 1253.5 cm^{2}

(d) none of them

**Answer**

C

**Question. A pendulum swings through an angle of 30° and describes an arc 8.8 cm is length. The length of the pendulum is **

(a) 16 cm

(b) 16.8 cm

(c) 16.4 cm

(d) none of them

**Answer**

B

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

(a) 330

(b) 400

(c) 360

(d) 300

**Answer**

D

**Question. A rectangular sheet of card board is 4 cm by 2 cm. The greatest possible circle is cut off form the card board then the remaining area is **

(a) (16 –π ) cm^{ 2}

(b) (16 – 4π ) cm^{ 2}

(c) (8 –π ) cm ^{2}

(d) none of them

**Answer**

C

**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 r_{1}^{2}+ r_{2}^{2} is **

(a) > r

^{2}

(b) =r

^{2}

(c) < r

^{2}

(d) none of them

**Answer**

B

**Question. Consider the statements below. **

(i) A quarter circle represents a sector of the circle.

(ii) A semicircle represents both sector and segment of the circle.

Which of these statements is correct?

(a) Only (i)

(b) Only (ii)

(c) Both (i) and (ii)

(d) Neither (i) nor (ii)

**Answer**

C

**Question. If the circumference of a circle increases from 4r to 8r , then the area is **

(a) halved

(b) doubled

(c) tripled

(d) quadrupled

**Answer**

D

**Question. ABC is an equailateral triangle. The area of the shaded region if the radius of each of the circle is 1 cm, is **

(a) 2-π/3

(b) √3 – π

(c) √3– π/2

(d) √3 -π/4

**Answer**

C

**Question. Which of these is equivalent to p? **

(a) Circumference/Radius

(b) Circumference/Diameter

(c) Circumference × Diameter

(d) Circumference × Radius

**Answer**

B

**Question. David draws a circle with diameter 6 units. He draws another circle by increasing the radius of the previously drawn circle by 4 units. What would be the quotient if he divides the circumference of the newly formed circle by its diameter? **

(a) 8

(b) 12

(c) π

(d) 2π

**Answer**

C

**Question. A circular garden, of circumference 88 m is surrounded by a pathway of width 3.5 m. Ajay wants to put fence around the pathway. What is the cost of fencing the pathway at the rate of ₹70 per metre? (Useπ= 22/7) **

(a) ₹ 3,080

(b) ₹ 3,850

(c) ₹ 6,160

(d) ₹ 7,700

**Answer**

D

**Question. A horse is placed for grazing inside a rectangular field 70 m by 52 m is tethered to one corner by a rope 21 m long. The area it can graze is **

(a) 340.5 cm^{2}

(b) 345 cm^{2}

(c) 346.5 cm^{2}

(d) none of them

**Answer**

C

**Question. A fountain is enclosed by a circular fence of circumference 11 m and is surrounded by a circular path. The circumference of the outer boundary of the path is 16 m. A gardener increased the width of the pathway by decreasing the area enclosed by the fence such that the length of the fence is decreased by 3 m. The path is to be covered by the bricks which cost ₹125 per m ^{2}. What will be the total cost, to the nearest whole number, required to cover the area by the bricks? (Useπ=22/7 ) **

(a) ₹ 1,910

(b) ₹ 9,878

(c) ₹ 39,772

(d) ₹ 79,545

**Answer**

A

**Question. Which of the following options represents the shaded region as the major sector and unshaded region as the minor sector? **

**Answer**

B

**Question. To form a circle of radius r, four minor sectors of equal measure are joined. Which of these options completes the sentence below? **

**The sum of the area of the four minor sectors is equal to the ___________.**

(a) area of the semicircle of diameter 2r.

(b) area of the circle of diameter 2r.

(c) circumference of the circle of radius r.

(d) circumference of the circle of diameter r.

**Answer**

B

**Question. To show the minor segment of a circle, a student shades the region enclosed between a chord and the minor arc. ****Which of these shows the region the student could have shaded? **

**Answer**

A

**Question. Which of these is equivalent to the sum of the lengths of arc corresponding to the minor and major segment of a circle of radius 12 cm? **

(a) 24π cm

(b) 48π cm

(c) 12π cm

(d) 144π cm

**Answer**

A

**Question. Observe the figure below:**

**What is the area of the segment PQR, if the radius of the circle is 7 cm? (Use π=22/7) **

(a) 14 cm^{2}

(b) 17.3 cm^{2}

(c) 28 cm^{2}

(d) 91 cm^{2}

**Answer**

A

**Question. Two concentric circles of radii 8 cm and 5 cm are shown below, and a sector forms an angle of 60° at the centre O. What is the area of the shaded region? **

(a) 38π/2

(b) 77π/2cm^{ 2}

(c) 195π/6 cm^{ 2}

(d) 295π/6 cm^{ 2}

**Answer**

C

**Question. An arc of a circle of radius 14 cm, subtends an angle of 45° at the centre as shown: **

**Which of these options is correct?**

(a) The arc shown is a minor arc and its length is 5.5 cm.

(b) The arc shown is a major arc and its length is 77 cm.

(c) The arc shown is a major arc and its length is 38.5 cm.

(d) The arc shown is a minor arc and its length is 11 cm.

**Answer**

D

**Question. A circle with centre O of diameter 28 cm and a chord BC of length 14 cm is shown below: **

**What is the length of the major arc of the circle, to the nearest tenth? 58**

(a) 14.7 cm

(b) 73.3 cm

(c) 146.7 cm

(d) 216.3 cm

**Answer**

B

**Question. An equilateral triangle of side 28 cm is inscribed in a circle of diameter 32 cm, as shown below: **

**What is the area of the shaded region? (Use π = 3.14 and √3 =1.73) **

(a) 75.68 cm^{2}

(b) 125.68 cm^{2}

(c) 411.84 cm^{2}

(d) 464.76 cm^{2}

**Answer**

D

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

(a) 55 m

(b) 110 m

(c) 220 m

(d) 230 m

**Answer**

C

**Question. The area of the incircle of an equilateral triangle of side 42 cm is **

(a) 22 √3 cm^{2}

(b) 231 cm^{2}

(c) 462 cm^{2}

(d) 924 cm^{2}

**Answer**

C

**Question. Consider a circle below. **

**Aman shades a part in the circle which is enclosed by two radii and its corresponding arc. Which of these could he have drawn?**

**Answer**

C

**Question. The area of the largest triangle that can be inscribed in a semicircle is **

(a) r^{2}

(b) 2r^{2}

(c) r^{3}

(d) 2r^{3}

**Answer**

A

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