CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set 07

Question. If a chord of a circle of radius 28 cm makes an angle of 900at the centre, then the area of the major segment is
(A) 392 cm²
(B) 1456 cm²
(C) 1848 cm²
(D) 2240 cm²

Answer: a

Question. The radius of circle is 20 cm. it is divided into four parts of equal area by drawing three concentric circles inside it. Then the radius of the largest of three concentric circles drawn is 
(A) 10√5cm
(B) 10√3cm
(C) 10 cm
(D) 10√2cm

Answer: b

Question. The area of a sector whose perimeter is four times its radius r units, is
(A) r²/4 sq units
(B) 2r² sq.units
(C) r² sq.units
(D) r²/2sq units

Answer: c

Question. Area of the largest triangle that can be inscribed in a semi –circle of radius r units is
(A) r²sq. units
(B) 1/2 r²sq. units
(C) 2r²sq. units
(D) √2r²sq. units

Answer: a

Question. If area of a circle inscribed in an equilateral triangle is 48π square units, Then perimeter of the triangle is 
(A) 17√3units
(B) 36 units
(C) 72 units
(D) 48√3

Answer: d

Question. If the area of a sector of a circle is 5/18 of the area of the circle, then the sector angle is equal to
(A) 600
(B) 900
(C) 1000
(D) 1200

Answer: c

Question. If the sum of the areas of two circles with radii 1 r and 2 r is equal to the area of a circle of radius r, then r²₁ + r²₂
(A) > r²
(B) =r²
(C) < r²
(D) None of these

Answer: b

Question. The area of a circle whose area and circumference are numerically equal, is
(A) 2π sq.units
(B) 4π sq.units
(C) 6π sq.units
(D) 8π sq.units

Answer: b

Question. The area of a circular path of uniform width h surrounding a circular region of radius r is
(A) π(2r + h)r
(B) π(2r + h)h
(C) π (h + r)r
(D) π(h + r)h

Answer: b

Question. If the area of a sector of a circle is 7/20 of the area of the circle, then the sector angle is equal to
(A) 1100
(B) 1300
(C) 1000
(D) 1260

Answer: d

Question. Find the area of a segment of a circle of radius 7 cm if the arc of the segment has measure 90°.
Solution. 14 cm²

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/hr?
Solution. 250

Question. A bicycle wheel makes 5,000 revolutions in moving 11 km. Find the diameter of the wheel.
Solution. 70 cm

Question. Find the area of the sector of a circle whose radius is 14 cm and angle of sector is 45°.
Solution. 77 cm²

Question. A copper wire, when bent in the form of a square, encloses an area of 484 cm2. If the same wire is bent in the form of a circle, find the area enclosed by it. [take π = 22/7]
Solution. 616 cm²

Question. An arc of length 20 π cm subtends an angle of 144° at the centre of the circle. Find the radius of the circle.
Solution. 25 cm

Question. A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm² . If the same wire is bent in the form of a circle, find the area of the circle.
Solution. 346.5 cm²

Question. A sector of a circle of radius 8 cm contains an angle of 135°. Find the area of the sector.
Solution. 24 π cm²

Question. The outer circumference of a circular racing track is 220 m. The track is everywhere 7 m wide. Calculate the cost of levelling the track at the rate of 50 paisa per sq. m.[use π = 22/7]
Solution. Rs. 693

Question. Find the area of the segment of a circle, given that the angle of the sector is 120° and the radius of the circle is 21 cm. [Take π = 22/7 and √3 = 1.73]
Solution. 271.2675 cm²

Question. The minute hand of a clock is 10 cm long. Find the area of the face of the clock described by the minute hand between 9:00 am and 9:35 am.
Solution. 183.3 cm²

Question. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. [use π = 3.14, √3 = 1.73]
Solution. 88.44 cm²

Question. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
Solution. 1254.96 cm²

Question. Three horses are tethered with 7 m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed.
Solution. 77 m2, 259 m2

Question. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. [use π = 3.14]
Solution. 189.97 km²

Question. The area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
Solution. 14 cm

Question. The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.
Solution. 45.03 m²

Question. An arc of a circle of radius 21 cm has a length of 17.6 cm. Find the angle subtended at the centre of the circle.
Solution. 48°

Question. A circle has been inscribed in a square of side 4 cm. Determine the left out area. What will be the left out area of the circle if a square is inscribed in the circle? [use π = 3.14]
Solution. 3.44 cm²; 4.56 cm²

Question. Find the radius of a circle whose area is equal to the sum of the areas of the three circles whose radii are 3 cm, 4 cm, and 12 cm.
Solution. 13 cm

Question. Two circles touch externally. The sum of their areas is 130 π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.
Solution. 11 cm and 3 cm

Question. A square is inscribed in a circle of radius 10 cm. Find the area of the circle, not included in the square [use π = 3.14]
Solution. 114 cm²

Question. A wheel of diameter 42 cm, makes 240 revolutions per minute. Find :
(i) the total distance covered by the wheel in one minute.
(ii) the speed of the wheel in km/hr.
Solution. (i) 316.8 m (ii) 19.008 km/hr

Question. Find the area of the circle whose circumference is 22 cm.
Solution. 38.5 cm²

Question. A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form. Find the length of the side of the square.
Solution. 44 cm

Question. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first?
Solution. 132 m

Question. A race track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. Find the width of the track.
Solution. 7 m

Question. A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road. [use π = 22/7]
Solution. 2618 m²

Question. In the given figure, ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region. 35
Solution. (16 π – 12 √3 ) cm²

Question. The side of a square is 42 cm. Find the area of (i) the inscribed circle (ii) the circumscribed circle.
Solution. (i) 1386 cm2 (ii) 2772 cm²

Question. In an equilateral triangle of side 12 cm, a circle is inscribed touching its sides. Find the area of the portion of the triangle not included in the circle. [use √3 =1.73 and π = 3.14]
Solution. 24.6 cm²

Question. Find the area of a quadrant of a circle whose circumference is 22 cm.
Solution. 9.625 cm²

Question. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find :
(i) Area of the minor sector
(ii) Area of the minor segment
(iii) Area of major sector
(iv) Area of major segment [use π = 3.14]
Solution. (i) 78.5 cm² (ii) 28.5 cm² (iii) 235.5 cm² (iv) 285.5 cm²