CBSE Class 10 Mathematics Areas related to circles MCQs Set D

Question. The perimeter of a circle is equal to twice that of square, then the ratio of their areas is: -
a) 22/7
b) 14/11
c) 7/22
d) 56/11

Answer: D

Question. The area of the square that can be inscribed in a circle of 10 cm radius is: -
a) 200 cm²
b) 128 cm²
c) 64√2 cm²
d) 64 cm²

Answer: A

Question. Area of a sector to circle of radius 6 cm is 9π  cm². Find the length arc of the corresponding arc of the circle is: -
a) 6π cm
b) 3 π cm
c) 5 π cm
d) 8 π cm

Answer: B

Question. A wheel has diameter 112 cm. The number of complete revolution it will take to cover 1056 m is: -
a) 100
b) 150
c) 200
d) 300

Answer: D

Question. The length of an arc of a circle with radius 12 cm is 10 π cm. The central angle of this arc is: -
a) 1200
b) 60
c) 750
d) 1500

Answer: D

Question. The area of a circle whose circumference 2π cm is: -
a) π  cm²
b) π/4 cm²
c) π/2 cm²
d) None of these

Answer: A

Question. In figure ‘o’ is the centre of a circle. The area of sector OAPB is 10/72 of the area of the circle find x.

a) 30o
b) 40o
c) 50o
d) 60o

Answer: C

Question. If the diameter of a semi-circular protractor is 28 cm, then find its perimeter.

a) 42 cm
b) 52 cm
c) 62 cm
d) 72 cm

Answer: D

Question. The diameter of a cycle wheel is 42 cm. How many rotations will it make to travel 1.98km?
a) 900
b) 1200
c) 1500
d) 1800

Answer: C

Question. The length of the minute hand of a clock is 15 cm. Find the area swept by the minute hand in 8 minutes.
a) 84.285 cm²
b) 94.285 cm²
c) 104.285 cm²
d) 114.285 cm²

Answer: B

Question. A copper wire when bent in the form of a square encloses an area of 225  cm². If the same wire is bent into the form of a circle, find the area of the circle (Use π =22/7).
a) 900/π cm²
b) π/900 cm²
c) 700/π cm²
d) π/700 cm²

Answer: A

Question. A wire is looped in the form of a circle of radius 14 cm. It is re-bent into a square form. Determine the side of the square (Use π = 22/7).
a) 12 cm
b) 22 cm
c) 32 cm
d) 42 cm

Answer: B

Question. ABC is a quadrant of circle of radius 28 cm and a semi-circle is drawn with BC as diameter. Find the area of Shaded region.

a) 192 cm²
b) 292 cm²
c) 392 cm²
d) 492 cm²

Answer: C

Question. The length of a minor arc is 2/8 of the circumference of the circle. Write the measure of the angle subtended by the arc at the centre of the circle.
a) 60^o
b) 70^o
c) 80^o
d) 90^o

Answer: D

Question. The area of an equilateral triangle is 9√3 cm². Taking each angular point as centre, circle is drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take √3=1.73]

a) 1.43 cm²
b) 1.33 cm²
c) 1.23 cm²
d) 1.13 cm²

Answer: A

Question. If the side of a square is 14 cm. find the area of circumscribed circle.
a) 68π cm²
b) 78π cm²
c) 88π cm²
d) 98π cm²

Answer: D

Question. If the side of a square is 16 cm. find the area of inscribed circle.
a) 54π cm²
b) 64π cm²
c) 74π cm²
d) 84π cm²

Answer: B

Question. If the radius of a circle is increased by 5%, then its area is increased by
a) 10%
b) 10.25%
c) 12.25%
d) 15.25%

Answer: B

Question. If the circumference of a circle is reduced by 15%, then its area is decreased by________.
a) 7.75%
b) 17.75%
c) 27.75%
d) 37.75%

Answer: C

Question. Area of the largest triangle that can be inscribed in a semi-circle of radius 3 units is______.
a) 3 sq units
b) 9 sq units
c) 12 sq units
d) 15 sq units

Answer: B

Question. In a circle of radius 21 cm, an arc subtends an angle of 60o at the centre, then the area of the sector is:
a) 211 cm²
b) 221 cm²
c) 231 cm²
d) 241 cm²

Answer: C

Question. The area of a circular path of uniform width of 3 meter surrounding a circular region of radius 10 meter is
a) 69π m²
b) 79π m²
c) 89π m²
d) 99π m²

Answer: A

(CASE STUDY BASED QUESTIONS)

1. In a village, there was no playground for children. If a child had to practice for any sports then thechildhad to go to the city stadium which is 20 km from the village. But village has a circular unused land and villagers decided to convert this unused land into a football ground, with athletic track around it, so that children can practice their choice of sports in village itself. Villagers also planned six seating areas with chairs (brown colour) and six seating area without chairs (grey colour) as shown in the figure. Athletic track (light blue) is between the football ground (light green) and seating area. The distance between the centre of the ground and the boundary of the stadium is 140 m, width of the athletic track is 30 m and AB is 20 m.

Based on the above case and figure, answer the following questions: -

Question. What is the area of the football ground?
a) 7100π m²
b) 6100π m²
c) 8100π m²
d) 9100π m²

Answer: C

Question. What is the length of the athletic track (inner boundary)?
a) 180π m
b) 190π m
c) 170π m
d) 160π m

Answer: A

Question. What is the length of the athletic track (outer boundary)?
a) 210π m
b) 220π m
c) 230π m
d) 240π m

Answer: D

Question. How much area is allocated for six seating corners with chairs?
a) 110600 (2π −3√3/12 )
b) 117600 (2π −3√3/12 )
c) 124600 (2π −3√3/12 )
d) 131600 (2π −3√3/12 )

Answer: B

Question. What is the total area allocated for athletic track?
a) 6300π m²
b) 5300π m²
c) 4300π m²
d) 3300π m²

Answer: A

Question. What is the total area used to develop this stadium?
a) 16600π
b) 17600π
c) 18600π
d) 19600π

Answer: D

2. In a school rangoli competition, Tanveer and his friends made a rangoli as shown in the following figure.
During the inspection, judges of the competition asked questions about the dimensions of the rangoli to his team. As the leader of the team, Raju replied that the rangoli is exactly in a circular shape. The points A, B, C, D, E, F, G, H, I, J, K, L are the points on the boundary of the rangoli and are at the equal distance with each other. All these points are directly attached with the centre O and are at a distance of 4 feet from O. To his reply, Judges again asked some specific questions as given in the figure.

Based on the facts provided by Raju and his team, answer the following questions and help the team to win the competition.

Question. What is the measurement of ∠LOI?
a) 80o
b) 100o
c) 90o
d) 70o

Answer: C

Question. What is the area of sector ADO?
a) 3π sq ft
b) 4π sq ft
c) 5π sq ft
d) 6π sq ft

Answer: B

Question. What is the area of segment ABCM?
a) 176/21 - 1√3 sq ft
b) 176/21 - 2√3 sq ft
c) 176/21 - 3√3 sq ft
d) 176/21 - 4√3 sq ft

Answer: D

Question. What is the area of ΔBOL?
a) 4√3 sq ft
b) 3√3 sq ft
c) 2√3 sq ft
d) 1√3 sq ft

Answer: A

Question. What is the ratio of area of sector ADO to area of circle with radius OA?
a) 4:1
b) 1:4
c) 1:5
d) 5:1

Answer: B

3. In a cycling race, the wheel of bicycle of the cyclist take total 304 rotation to complete the circuit. The cycling track is around the Football ground that is of rectangular shape with semi-circular shape on both side. The perimeter of the inner rectangular ground is 496 m. The inner semi-circular shape on both side has a length of 154 m each (from A to I to J or from C to L to D). The width of the track is 7 m.

Question. What is the area of the Football field?
a) 22246 m²
b) 23246 m²
c) 21246 m²
d) 22346 m²

Answer: A

Question. What is the length of the Football ground (From I to L)?
a) 148 m
b) 208 m
c) 348 m
d) 248 m

Answer: D

Question. What is the radius of the wheel of bicycle?
a) (8/21) m
b) (7/22) m
c) (7/21) m
d) (9/22) m

Answer: B

Question. What is the area of Cycling track?
a) 4420 m²
b) 4310 m²
c) 4410 m²
d) 4415 m²

Answer: C

Question. In how many rounds the cyclist will cover 12 km distance?
a) 6000 rounds
b) 5000 rounds
c) 4000 rounds
d) 3000 rounds

Answer: A

4. Kritvi invited her best friends on her birthday. Her parents ordered a birthday cake for the occasion. The diameter of the cake ordered is 18 inch and its 3 kg 600 grams in weight. She wanted to distribute this cake equally among all the persons present in the party in such a way that cake will be used up completely.

Question. What is the area of the top surface of the cake?
a) 72π
b) 63π
c) 81π
d) 91π

Answer: C

Question. If each piece cut has an angle of 60o, how many persons are there in the party, if each 60o piece cut is distributed among three persons.
a) 18
b) 20
c) 22
d) 24

Answer: A

Question. What is the weight of each piece distributed to each person, if cake has equal density?
a) 50 gm
b) 100 gm
c) 150 gm
d) 200 gm

Answer: D

Question. What is the top perimeter of each 60o slice?
a) 27.42 inch
b) 17.42 inch
c) 37.42 inch
d) 07.42 inch

Answer: A

Question. If there were 20 persons in party and same size piece to be offered to everyone, then what should be the weight of the cake ordered.
a) 1 kg
b) 3 kg
c) 4 kg
d) 2 kg

Answer: C

5. A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around each horse and let them freely move and graze separately in their own area. (π = 3.14) Find: -

Question. The total area of the field in which these horses can graze. (π = 22/7)
a) 104 m²
b) 154 m²
c) 134 m²
d) 164 m²

Answer: B

Question. How much the length of the rope of each horse be increased so that they can graze in maximum area without encroaching in each other’s area (new length of rope after increase).
a) 10 m
b) 5 m
c) 15 m
d) 20 m

Answer: A

Question. What is the area of the field that is left un-grazed after increasing the length of the rope? (π = 3.14)
a) 86 m²
b) 76 m²
c) 106 m²
d) 96 m²

Answer: A

Question. If the length of the rope is increased as per part (ii) above, find the cost of fencing around every horse so that the owner leave these horses untied inside these fenced areas, if the cost per meter length of the fencing is ₹50.
a) ₹3148
b) ₹2140
c) ₹3140
d) ₹2140

Answer: C

6. An Umbrella frame is made with steel wire. It has 8 spokes which are equally spaced. If these spokes are expanded fully they are in the form of a circle with diameter of 4 meters. Steel wire is used in making the ribs and the outer frame of the umbrella to which these ribs are attached. Find:

Question. The total length of the Steel wire used is _____________.
a) 08.571 m
b) 11.571 m
c) 18.571 m
d) 28.571 m

Answer: D

Question. The area between the three consecutive spokes of the umbrella _____________.
a) π m²
b) 2π m²
c) 3π m²
d) 4π m²

Answer: A

Question. The angle between any two spoke of the umbrellais _____________.
a) 30o
b) 45o
c) 60o
d) 75o

Answer: B

Question. How much water proof cloth was used in making this umbrella.
a) 2π m²
b) 3π m²
c) 4π m²
d) 5π m²

Answer: C

7. In a wall clock (as shown in the figure) the length of the minute hand is 3 cm less than the radius of the upper semi-circular part of the clock. The circumference of the semi-circular upper part is 6 cm less than the perimeter of the lower equilateral triangular part. If the circumference of the semi-circular part is 36 cm. Then find the: -

Question. The Length of the minute hand.
a) 4 cm
b) 6 cm
c) 8 cm
d) 10 cm

Answer: A

Question. Area of the equilateral lower part. (use√3 = 1.73)
a) 74.77 cm²
b) 84.77 cm²
c) 94.77 cm²
d) 104.77 cm²

Answer: B

Question. Area of the upper semi-circular part.
a) 57 cm²
b) 67 cm²
c) 77 cm²
d) 87 cm²

Answer: B

Question. Area of the figure.
a) 131.77 cm²
b) 141.77 cm²
c) 151.77 cm²
d) 161.77 cm²

Answer: D

8. Ferris Wheel in an amusement park has cabins attached in the outer ring (Saffron colour), it has five spokes that are fixed at the centre (circular solid centre) and are attached to the outer ring (carrying sitting cabins) as shown in the below pictures. Inner circular centre has radius = R1, the central circular space has width = R2, the width of the outer ring = w and R3 = R1 + R2 + W. If R1 = 1 meter, R2 = 5 meter and W = 2 meter, then: -

Question. Find the area occupied between any two spokes excluding the area of the width of the spoke (Assume that the all spokes start from the center O).
a) 13.52 m²
b) 3.52 m²
c) 23.52 m²
d) 33.52 m²

Answer: D

Question. Find the area occupied by the outer ring.
a) 68 m²
b) 78 m²
c) 88 m²
d) 98 m²

Answer: C

Question. In how many rotations this Ferris Wheel will cover 10 Km?
a) 188.88 rotations
b) 198.88 rotations
c) 208.88 rotations
d) 218.88 rotations

Answer: B

Question. If in 30 seconds the wheel completes 1 rotation and on a single ticket a person is allowed for only 10 minutes. What is the distance covered by this wheel on single ticket?
a) 1005.6 meters
b) 1015.6 meters
c) 1025.6 meters
d) 1035.6 meters

Answer: A