CBSE Class 10 Mathematics Area Relates to Circles Assignment Set B

Question. The perimeter of a sector of a circle with central angle 90° is 25 cm. Then the area of the minor segment of the circle is.
(a) 14 cm²
(b) 16 cm²
(c) 18 cm²
(d) 24 cm²

Answer: A

Question. The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm respectively is
(Take π = 3.1416)
(a) 43.98 sq.cm
(b) 53.67 sq. cm
(c) 47.24 sq.cm
(d) 38.54 sq.cm

Answer: A

Question. A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240º. If another circle of the area same as the sector is formed, then radius of the new circle is
(a) 79.5 cm
(b) 81.6 cm
(c) 83.4 cm
(d) 88.5 cm

Answer: B

Question. The area of a sector of angle p (in degrees) of a circle with radius R is
(a) P/360° × 2πR
(b) P/180° × 2πR²
(c) P/720° × 2πR
(d) P/720° × 2πR²

Answer: D

Question. The sum of the areas of two circles, which touch each other externally, is 153 π. If the sum of their radii is 15, then the ratio of the larger to the smaller radius is
(a) 4 : 1
(b) 2 : 1
(c) 3 : 1
(d) None of these

Answer: A

Question. A race track is in the form of a ring whose inner and outer circumference are 437m and 503m respectively. The area of the track is
(a) 66 sq. cm
(b) 4935 sq. cm
(c) 9870 sq. cm
(d) None of these

Answer: B

Question. If the sum of the circumferences of two circles with diameters d₁ and d₂ is equal to the circumference of a circle of diameter d, then
(a) d₁² + d²₂ = d²
(b) d₁ + d₂ = d
(c) d₁ + d₂ > d
(d) d₁ + d₂ < d

Answer: B

Question. If the sector of a circle of diameter 10 cm subtends an angle of 144° at the centre, then the length of the arc of the sector is
(a) 2π cm
(b) 4π cm
(c) 5π cm
(d) 6π cm

Answer: B

Question. Find area of minor segment made by a chord which subtends right-angle at the centre of a circle of radius 10 cm.
(a) 24.5 cm²
(b) 25.5 cm²
(c) 24.5 cm²
(d) 28.5 cm²

Answer: D

Question. A drain cover is made from a square metal plate of side 40 cm having 441 holes of diameter 1 cm each drilled in it. Find the area of the remaining square plate.
(a) 1250.5 cm²
(b) 1253.5 cm²
(c) 1240.2 cm²
(d) 1260.2 cm²

Answer: B

Question. If a circular grass lawn of 35m in radius has a path 7m wide running around it on the outside, then the area of the path is
(a) 1450 m²
(b) 1576 m²
(c) 1694 m²
(d) 3368 m²

Answer: C

Question. The area of a circular path of uniform width ‘d’ surrounding a circular region of radius ‘r’ is
(a) πd(2r + d)
(b) π(2r + d) r
(c) π(d + r)d
(d) π(d + r)r

Answer: A

Question. If Anish is moving along the boundary of a triangular field of sides 35 m, 53 m and 66 m and you are moving along the boundary of a circular field whose area is double the area of the triangular field, then the radius of the circular field is (Take π = 22/7)
(a) 14V3 m
(b) 3√14 m
(c) 28√3 m
(d) 7√3 m

Answer: A

Question. If the area of a square inscribed in a semicircle is 2cm², then the area of the square inscribed in a full circle of the same radius is ______
(a) 5 cm²
(b) 10 cm²
(c) 5√2 cm²
(d) 25 cm²

Answer: A

Question. Suppose we have two circles of radius 2 each in the plane such that the distance between their centers is 2√3. The area of the region common to both circles lies between
(a) 0.5 and 0.6
(b) 0.65 and 0.7
(c) 0.7 and 0.75
(d) 0.8 and 0.9

Answer: C

Question. If the circumference of a circle increases from 4π to 8π, then its area is
(a) halved
(b) doubled
(c) tripled
(d) quadrupled

Answer: D

Question. If the radius of a circle is diminished by 10%, then its area is diminished by
(a) 10%
(b) 19%
(c) 36%
(d) 20%

Answer: B

Question. If the perimeter of a semi-circular protractor is 36 cm, then its diameter is
(a) 10 cm
(b) 14 cm
(c) 12 cm
(d) 16 cm

Answer: B

Question. A circle is inscribed in a right angled triangle of perimeter 7π . Then the ratio of numerical values of circumference of the circle to the area of the right angled triangle is
(a) 4 : 7
(b) 3 : 7
(c) 2 : 7
(d) 1 : 7

Answer: A

Question. How much time the minute hand of a clock will take to describe an angle of 2π/3 radians?
(a) 15 minutes
(b) 20 minutes
(c) 10 minutes
(d) 25 minutes

Answer: B

Question. If the radius of a circle is (7/√π) cm, then the area of the circle is equal to
(a) (49/π)cm²
(b) p cm²
(c) 154 cm²
(d) 49 cm²

Answer: D

Question. Which of the following statement is/are not correct?
(a) A chord divides the interior of a circle into two parts.
(b) An arc of a circle whose length is less than that of a semicircle of the same circle is a called a minor arc.
(c) Circles having the same centre but different radii are called concentric circles.
(d) A line segment joining any two points of a circle is called an arc.

Answer: D

Question. Tick the correct answer in the following and justify your choice. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(a) 2 units
(b) π units
(c) 4 units
(d) 7 units

Answer: A

Question. If θ is the angle (in degree) of a sector of a circle of radius r, then, area of the sector is
(a) πr²θ/360°
(b) πr²θ/180°
(c) 2πr²θ/360°
(d) 2πr²θ/180°

Answer: A

Question. If the ratio of the areas of the two circles is 25 : 16, then the ratio of their circumferences is
(a) 25/16
(b) 4/5
(c) 5/4
(d) 500/625

Answer: C

Question. If the sector of a circle of diameter 14cm subtends an angle of 30° at the centre, then its area is
(a) 49π
(b) 49π/12
(c) 242π/3
(d) 121/π

Answer: B

Question. Which of the following is/are not correct?
(a) Area of a circle with radius 6 cm, if angle of sector is 60°, is (132/14) cm².
(b) If a chord of circle of radius 14 cm makes an angle of 60° at the centre of the circle, then area of major sector is 512.87 cm².
(c) The ratio between the circumference and area of a circle of radius 5 cm is 2 : 5.
(d) Area of a circle whose radius is 6 cm, when the length of the arc is 22 cm, is 66 cm2.

Answer: A

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: B

DIRECTIONS : Study the given Case/Passage and answer the following questions.

Case/Passage-I

Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu.
During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below. Observe these carefully.

Design I: This design is made with a circle of radius 32cm leaving equilateral triangle ABC in the middle as shown in the given figure.
Design II: This Pookalam is made with 9 circular design each of radius 7cm.

Question. The side of equilateral triangle is
(a) 12√3 cm
(b) 32√3 cm
(c) 48 cm
(d) 64 cm

Answer: B

Question. The altitude of the equilateral triangle is
(a) 8 cm
(b) 12 cm
(c) 48 cm
(d) 52 cm

Answer: C

Question. The area of square is
(a) 1264 cm²
(b) 1764 cm²
(c) 1830 cm²
(d) 1944 cm²

Answer: B

Question. Area of each circular design is
(a) 124 cm²
(b) 132 cm²
(c) 144 cm²
(d) 154 cm²

Answer: D

Question. Area of the remaining portion of the square ABCD is
(a) 378 cm²
(b) 260 cm²
(c) 340 cm²
(d) 278 cm²

Answer: A

Case/Passage-II

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A: Brooch A is made with silver wire in the form of a circle with diameter 28mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.
Design B: Brooch b is made two colours-Gold and silver. Outer part is made with Gold. The circumference of silver part is 44mm and the gold part is 3mm wide everywhere.

Question. The total length of silver wire required is
(a) 180 mm
(b) 200 mm
(c) 250 mm
(d) 280 mm

Answer: B

Question. The area of each sector of the brooch is
(a) 44 mm²
(b) 52 mm²
(c) 77 mm²
(d) 68 mm²

Answer: C

Question. The circumference of outer part (golden) is
(a) 48.49 mm
(b) 82.2 mm
(c) 72.50 mm
(d) 62.86 mm

Answer: D

Question. The difference of areas of golden and silver parts is
(a) 18 π
(b) 44 π
(c) 51 π
(d) 64 π

Answer: C

Question. A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 p mm ?
(a) 2
(b) 3
(c) 4
(d) 5