Areas Related to Circles

What is the formula for the area of a circle with radius r?

a)
πr3
b)
2πr
c)
πr2
d)
πr2
Answer: c)
πr2
What is a sector of a circle?
a) A part of a circle enclosed by two radii and an arc
b) A chord of a circle
c) A line outside the circle
d) The entire circle
Answer: a) A part of a circle enclosed by two radii and an arc
If the angle of a sector is

90∘90^\circ

what fraction of the circle does the sector represent?
a)
14
b)
12
c)
13
d)
16
Answer: a)
14
What is the name of the area enclosed between a chord and the corresponding arc?
a) Segment
b) Sector
c) Tangent
d) Diameter
Answer: a) Segment
The length of the arc of a sector is proportional to what?
a) Radius of the circle
b) The angle of the sector
c) Diameter of the circle
d) Circumference of the circle
Answer: b) The angle of the sector
Find the area of a sector of a circle with radius 7 cm and angle

60∘60^\circ

Use

π=227
a) 25.66 cm²
b) 30 cm²
c) 35 cm²
d) 40 cm²
Answer: a) 25.66 cm²
The area of a quadrant of a circle with radius 14 cm is:
a)
154 cm2
b)
308 cm2
c)
77 cm2
d)
616 cm2
Answer: a)
154 cm2
What is the length of the arc of a sector with angle

90∘90^\circ

and radius 10 cm? Use $π = 3.14$ .
a) 15.7 cm
b) 20 cm
c) 31.4 cm
d) 25 cm
Answer: a) 15.7 cm
A chord of a circle with radius 10 cm subtends a right angle at the center. Find the area of the minor sector.
a)
78.5 cm2
b)
31.4 cm2
c)
50 cm2
d)
25 cm2
Answer: a)
78.5 cm2
If the circumference of a circle is 22 cm, what is the radius?
a) 3 cm
b) 3.5 cm
c) 4 cm
d) 4.5 cm
Answer: b) 3.5 cm
Find the area of the segment formed by a chord of length 14 cm in a circle with radius 10 cm. Use π=3.14 and

3=1.73
a) 48 cm²
b) 50 cm²
c) 55 cm²
d) 60 cm²
Answer: b) 50 cm²
In a circle of radius 15 cm, an arc subtends an angle of

60∘60^\circ

at the center. Find the area of the corresponding sector. Use π=3.14

a) 117.75 cm²
b) 125 cm²
c) 130 cm²
d) 140 cm²
Answer: a) 117.75 cm²
A circle of radius 21 cm has a chord subtending an angle of

120∘120^\circ

at the center. Find the area of the minor segment. Use

π=227
a) 220 cm²
b) 240 cm²
c) 250 cm²
d) 260 cm²
Answer: b) 240 cm²
A horse is tied with a 10 m long rope at the corner of a square field of side 20 m. Find the grazing area available to the horse. Use

π=3.14
a) 78.5 m²
b) 157 m²
c) 314 m²
d) 628 m²
Answer: b) 157 m²
Find the total length of the silver wire required to form a circular brooch with a diameter of 35 mm and 5 internal diameters.
a) 245 mm
b) 280 mm
c) 315 mm
d) 350 mm
Answer: c) 315 mm
The minute hand of a clock is 14 cm long. Find the area swept by the minute hand in 10 minutes. Use

π=227
a) 51.33 cm²
b) 102.67 cm²
c) 154 cm²
d) 205.33 cm²
Answer: b) 102.67 cm²
An umbrella with 8 ribs has a radius of 45 cm. Find the area between two consecutive ribs. Use

π=3.14
a) 158.63 cm²
b) 254.34 cm²
c) 318.75 cm²
d) 452.16 cm²
Answer: a) 158.63 cm²
A lighthouse spreads red light over a sector of angle

80∘80^\circ

to a distance of 16.5 km. Find the area of the sea covered by the light. Use

π=3.14
a) 190.96 km²
b) 227.68 km²
c) 284.34 km²
d) 318.75 km²
Answer: b) 227.68 km²
A car’s wiper blade sweeps an angle of

115∘115^\circ

with a length of 25 cm. Find the total area cleaned by the two wipers. Use

π=3.14
a) 627.5 cm²
b) 785 cm²
c) 942.5 cm²
d) 1000 cm²
Answer: a) 627.5 cm²
Find the cost of making designs on a round table cover of radius 28 cm at

₹0.35/cm2\text{₹} 0.35/\text{cm}^2

Use

π=3.14\pi = 3.14

and

3=1.73
a)
₹860
b)
₹940
c)
₹1232
d)
₹1720
Answer: c)
₹1232
What is the angle of a complete circle in degrees?
a)
90∘
b)
180∘
c)
270∘
d)
360∘
Answer: d)
360∘
What is the length of an arc of a semicircle with radius 7 cm? Use

π=227
a) 22 cm
b) 33 cm
c) 44 cm
d) 66 cm
Answer: a) 22 cm
What fraction of a circle is a quadrant?
a)
12
b)
14
c)
16
d)
18
Answer: b)
14
If the radius of a circle is doubled, by what factor does its area increase?
a) 2
b) 3
c) 4
d) 6
Answer: c) 4
The formula for the length of an arc is:
a)
θ360⋅πr2
b)
θ360⋅2πr
c)
θ180⋅πr
d)
θ90⋅2πr
Answer: b)
θ360⋅2πr
Find the area of a semicircle with a radius of 7 cm. Use

π=227
a) 77 cm²
b) 154 cm²
c) 38.5 cm²
d) 308 cm²
Answer: a) 77 cm²
A circle has a radius of 21 cm. Find the length of an arc that subtends an angle of

120∘120^\circ

Use

π=227
a) 22 cm
b) 44 cm
c) 66 cm
d) 88 cm
Answer: c) 66 cm
The area of a segment of a circle is given by:
a)
Area of sector−Area of triangle
b)
12⋅πr2
c)
θ360⋅2πr
d)
πr2−Area of triangle
Answer: a)
Area of sector−Area of triangle
The radius of a circle is 14 cm. Find the area of a sector that subtends an angle of

60∘60^\circ

Use

π=227
a) 51.33 cm²
b) 102.67 cm²
c) 154 cm²
d) 205.33 cm²
Answer: b) 102.67 cm²
What is the area of a quadrant of a circle with radius 10 cm? Use

π=3.14
a) 50 cm²
b) 78.5 cm²
c) 25 cm²
d) 100 cm²
Answer: b) 78.5 cm²
A chord of a circle with radius 15 cm subtends an angle of

90∘90^\circ

at the center. Find the area of the minor segment. Use

π=3.14
a) 72.75 cm²
b) 98.5 cm²
c) 120 cm²
d) 135 cm²
Answer: a) 72.75 cm²
Find the area of the sector of a circle with radius 10 cm and angle

135∘135^\circ

Use

π=3.14
a) 117.75 cm²
b) 150 cm²
c) 117 cm²
d) 135 cm²
Answer: a) 117.75 cm²
The radius of a circle is 7 cm. A chord subtends an angle of

120∘120^\circ

at the center. Find the area of the minor segment. Use

π=227\pi = \frac{22}{7}

and

3=1.73
a) 30.73 cm²
b) 35.5 cm²
c) 40 cm²
d) 50.5 cm²
Answer: a) 30.73 cm²
The length of an arc is 11 cm in a circle with a radius of 7 cm. Find the angle subtended by the arc at the center. Use

π=227
a)
90∘
b)
120∘
c)
135∘
d)
180∘
Answer: b)
120∘
A brooch is made with silver wire in the form of a circle with diameter 28 mm. Five diameters divide the circle into 10 equal sectors. Find the area of each sector. Use

π=227
a) 61.6 mm²
b) 43.96 mm²
c) 71.68 mm²
d) 80 mm²
Answer: b) 43.96 mm²
A circle is inscribed in a triangle. The sides of the triangle are 6 cm, 8 cm, and 10 cm. Find the radius of the circle.
a) 1 cm
b) 2 cm
c) 3 cm
d) 4 cm
Answer: b) 2 cm
Find the area of a sector of a circle of radius 21 cm if the angle of the sector is

210∘210^\circ

Use

π=227
a) 808.5 cm²
b) 693 cm²
c) 485 cm²
d) 726 cm²
Answer: a) 808.5 cm²
The angle of a sector is

120∘120^\circ

in a circle with radius 14 cm. Find the perimeter of the sector. Use

π=227
a) 44 cm
b) 51 cm
c) 58 cm
d) 62 cm
Answer: b) 51 cm
A car wiper blade is 20 cm long and sweeps an angle of

120∘120^\circ

Find the area cleaned by one blade per sweep. Use

π=3.14
a) 125.6 cm²
b) 150.72 cm²
c) 200 cm²
d) 251.2 cm²
Answer: b) 150.72 cm²
Find the area of a circular track with an inner radius of 14 m and an outer radius of 21 m. Use

π=227
a) 385 m²
b) 462 m²
c) 154 m²
d) 616 m²
Answer: a) 385 m²
The cost of polishing a circular table top with a diameter of 1.4 m is $₹ 50$ per m². Find the total cost. Use
π=3.14
a) ₹ 77
b) ₹98
c) ₹154
d) ₹176
Answer: b) ₹98
Find the angle subtended by an arc at the center of a circle with radius 28 cm if the length of the arc is 44 cm. Use
π=227
a)
60∘60^\circ

b)
75∘75^\circ

c)
90∘90^\circ

d)
120∘120^\circ

Answer: c)
90∘90^\circ
Find the length of an arc of a circle with radius 15 cm and angle
270∘270^\circ
Use $π = 3.14$ .
a) 70.65 cm
b) 79.5 cm
c) 84.9 cm
d) 95 cm
Answer: b) 79.5 cm
A sector of a circle has an area of
77 cm277 \, \text{cm}^2
The angle of the sector is
90∘90^\circ
Find the radius of the circle. Use
π=227
a) 7 cm
b) 10 cm
c) 14 cm
d) 21 cm
Answer: a) 7 cm
A chord of a circle with radius 10 cm subtends an angle of
60∘60^\circ
at the center. Find the area of the corresponding minor segment. Use
π=3.14
a) 16.75 cm²
b) 23.5 cm²
c) 30.5 cm²
d) 35 cm²
Answer: b) 23.5 cm²
A lighthouse spreads light over a sector of
120∘120^\circ
to a distance of 30 km. Find the area of the sea over which the light spreads. Use
π=3.14
a) 942 km²
b) 1800 km²
c) 3140 km²
d) 6280 km²
Answer: a) 942 km²
A square field has a side of 20 m. A circular path of radius 14 m is inscribed within the field. Find the remaining area of the field. Use
π=227
a) 72 m²
b) 80 m²
c) 100 m²
d) 150 m²
Answer: c) 100 m²
The radius of a circular park is 35 m. Find the cost of fencing it at $₹ 20$ per meter. Use
π=227\pi = \frac{22}{7}

a) ₹2200
b) ₹4400
c) ₹6600
d) ₹8800
Answer: b) ₹4400
Find the angle subtended at the center by a chord of length 10 cm in a circle with radius 7 cm. Use
π=3.14
a)
90∘
b)
120∘
c)
60∘
d)
45∘
Answer: c)
60∘
A circular fountain of radius 14 m is surrounded by a 7 m wide path. Find the area of the path. Use
π=227
a) 462 m²
b) 693 m²
c) 154 m²
d) 308 m²
Answer: b) 693 m²