CBSE Class 10 Mathematics Areas Related to Circles VBQs

Question. The area of the circle that can be inscribed in the square of side 6cm is
(a) 18𝜋𝑐𝑚
(b) 12𝜋𝑐𝑚
(c) 9𝜋𝑐𝑚
(d) 14𝜋𝑐𝑚
Answer : C

Question. A wire is looped in the form of a circle of radius 28 cm. It is re-bent into a square form.
Determine the length of the side of the square:-
(a) 42 cm
(b) 44 cm
(c) 46 cm
(d) 48 cm
Answer : B

Question. Find the area of a right angled triangle, if the radius of its circumscribed circle is 2.5 cm and the altitude drawn to the hypotenuse is 2 cm long.
(a) 5 cm²
(b) 6 cm²
(c) 7 cm²
(d) none of these
Answer : A

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. What is the area of the circle that can be inscribed in a square of side 6 cm?
(a) 9 π cm²
(b) 11 π cm²
(c) 16 π cm²
(d) 15 π cm²
Answer : A

Question. The area of a quadrant of a circle whose circumference is 25 cm is
(a) 24 cm²
(b) 28 cm²
(c) 32.5 cm²
(d) 38.5 cm²
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. A square is inscribed in a circle of radius r. Find the area of the square in sq.units
(a) 3r²
(b) 2r²
(c) 4r²
(d) none of these
Answer : B

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. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm²
(b) 128 cm²
(c) 64 2√2 cm
(d) 64 cm²
Answer : B

Question. The area of the square is the same as the area of the circle. Their perimeter are in the ratio:-
(a) 1:1
(b) 𝜋:2
(c) 2:𝜋
(d) none of these
Answer : D

Question. The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.
(a) 44 cm²
(b) 44.6 cm²
(c) 44.8 cm²
(d) none of these
Answer : C

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. 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 area of circle whose circumference is 22 cm is
(a) (32/2)cm²
(b) (45/2)cm²
(c) (55/2)cm²
(d) (77/2)cm²
Answer : D

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 m²
(b) 340 m²
(c) 550 m²
(d) 770 m²
Answer : D

Question. A road which is 7 m wide surrounds a circular park whose circumference is 352 m.
Find the area of the roa(d)
(a) 2618 m²
(b) 2518 m²
(c) 1618 m²
(d) none of these
Answer : A

Question. In making 1000 revolutions, a wheel covers 88 Km. The diameter of the wheel is:-
(a) 14 m
(b) 24 m
(c) 28 m
(d) 40 m
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. 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. Area of a sector of a circle of radius R, whose central angle is P (in degrees) is given by:
(a) 𝑃/180 x 2πR
(b) 𝑃/180 x π𝑅²
(c) 𝑃/180 x 2π𝑅²
(d) 𝑃/360 x 2π𝑅
Answer : C

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) r² sq. units
(d) 2r sq. units
Answer : C
 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): If the circumference of a circle is 176 cm, then its radius is 28 cm.
Reason (R): Circumference = 2p × radius.
Answer : A

Question. Assertion (A): If the outer and inner diameter of a circular path is 10 m and 6 m respectively, then area of the path is 16 p m².
Reason (R): If R and r be the radius of outer and inner circular path respectively, then area of circular path = p (R² – r²).
Answer : A
 

Very Short Answer Type Questions

Question. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Answer : (154/3)cm

Question. A car has two wipers which do not overlap. Each wiper has a blade length of 25 cm and sweeping through an angle of 115˚. What will be the total area of the glass wiped at each sweep of the wiper blades.
Answer : 1254.96 sq.cm

Question. The difference between the radii of the smaller circle and the larger circle is 7 cm and the difference between the areas of the two circles is 1078 sq.cm. Find the radius of the smaller circle.
Answer : r = 21 cm

Question. The circumference of a circle exceeds the diameter by 16.8 cm. Find the radius of the circle.
Answer : 3.92 cm

Question. Diameter of a garden roller is 1.4 m. Find the cost of painting both circular faces of the roller at the cost of ₹ 120 per sq. m. (Take π = 22/7 )
Answer : Rs.369.6

Question. Find the ratio of area of the circle circumscribing a square to the area of a circle inscribed in the square.
Answer : 2:1

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 9 A.M and 9.35 A.M.
Answer : 183.3 sq.cm

Question. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distances travelled by their tips in 2 days.
Answer : 1910.85 cm

Question. A square of diagonal 18 cm is inscribed in a circular plate. The square portion is cut using a LASER cutter and taken out. Find the area of the remaining portion of the circular plate.
Answer : 92.57 sq.cm

Question. The central angles of two sectors of circles of radii 7cm and 21 cm are respectively 1200 and 400.Find the areas of the two sectors as well as the length of the corresponding arcs. What do you observe?
Answer : 154/3,154,44/3,44/3arc lengths of 2 circles of diff. Radii may be same but areas need not be equal.

Question. In a circle with centre O and radius 5cm, AB is a chord of length 5√3 cm. Find the area of sector AOB.
Answer : (25𝜋/3)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.
Answer : (158125/126) cm

Question. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
Answer : 20.4375 cm² ; 686.0625 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 and √3 = 1.73)
Answer : 88.44 cm²

Question. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Answer : (132/7) cm²

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)
Answer : 189.97 km²

Question. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding
(i) minor segment (ii) major sector. (Use π = 3.14)
Answer : (i) 28.5 cm2 (ii) 235.5 cm2

Question. The sum of the areas of two circle, which touch each other externally, is 153 . If the sum of their radii is 15, then find the ratio of the larger to the smaller radius .
Answer : 4:1

Question. An arc of a circle is of length 5 π cm and the sector it bounds has an area of 25 sq cm .Find radius of circle.
Answer : 8 cm

Question. The circumference of two circles are in the ratio 2:3. Then find ratio of their areas.
Answer : 4 : 9

Question. Find the area of sector of central angle x° of a circle with radius 4r.
Answer : (2𝜋𝑥𝑟2/45°)cm²

Question. On increasing the diameter of circle by 40%,find how much its area will be increased?
Answer : 96%

Question. The minute hand of a clock is 12 cm long ,find the area swept by minute hand in 35 minutes. .
Answer : 264 cm²

Question. If the radius of a circle is diminished by 10%, then find how much area will diminished ?
Answer : 36%

Question. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find length of the arc.
Answer : 22 cm