Mathematics Questions and Answers – Area of Sector and Segment of a Circle

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Area of Sector and Segment of a Circle”.

1. What is the name of the sector with a larger area?
a) Large
b) Major
c) Big
d) Wide
View Answer

Answer: b
Explanation: A sector is a part of a circle that is enclosed by two radii and an arc. The sector having a larger area is called a major sector and the sector having a smaller area is called a minor sector.
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2. What is the name of the sector with a smaller area?
a) Small
b) Narrow
c) Minor
d) Tiny
View Answer

Answer: c
Explanation: A sector is a part of a circle that is enclosed by two radii and an arc. The sector having a larger area is called a major sector and the sector having a smaller area is called a minor sector.

3. What is the formula to calculate the area of a sector?
a) \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
b) \(\frac {x^{\circ }}{360^{\circ }}\) + πr2
c) \(\frac {x^{\circ }}{360^{\circ }}\) – πr2
d) \(\frac {x^{\circ }}{360^{\circ }}\) × πr3
View Answer

Answer: a
Explanation: The area of the sector is \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
Where x° is the degree measure of the angle at the center and r is the radius of the circle.
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4. Find the area of the sector if the radius is 5 cm and with an angle of 50°.
a) 11.90 cm
b) 10.90 cm
c) 12.90 cm
d) 13.90 cm
View Answer

Answer: b
Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
= \(\frac {50^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 52
= 10.90 cm

5. Find the area of the sector if the radius is 12 cm and with an angle of 134°.
a) 158.38 cm
b) 168.00 cm
c) 167.38 cm
d) 168.38 cm
View Answer

Answer: d
Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
= \(\frac {134^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 122
= 168.38 cm
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6. A man goes to a walking track twice a day in the shape of a sector with an angle of 123° and a radius of 138 m. Find the area covered by the man of the walking track in a day.
a) 20441.4 m
b) 20882.8 m
c) 40882.8 m
d) 81765.6 m
View Answer

Answer: c
Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
= \(\frac {123^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 1382
= 20441.4 m
Area covered by the man of the walking track in a day = 20441.4 + 20441.4
= 40882.8 m

7. A horse is grazing in a field. It is tied to a pole with a rope of length 6 m. The horse moves from point A to point B making an arch with an angle of 70°. Find the area of the sector grazed by the horse.
a) 20.99 m
b) 21.99 m
c) 22.99 m
d) 23.99 m
View Answer

Answer: b
Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr2
= \(\frac {70^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 62
= 21.99 m
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8. Number of sectors in a circle are ____
a) 2
b) 3
c) 4
d) 1
View Answer

Answer: a
Explanation: A circle contains two sectors. The sector having a larger area is called a major sector and the sector having a smaller area is called a minor sector.

9. A segment is a part of a circle that is enclosed by two radii and an arc.
a) False
b) True
View Answer

Answer: a
Explanation: A segment is a part of a circle that is obtained by subtracting the triangle from the sector whereas, a sector is part of a circle that is enclosed by two radii and an arc.
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10. Find the area of the segment if the area of the sector is 44 m and the part of a triangle in the sector is 12 m.
a) 39 m
b) 22 m
c) 32 m
d) 31 m
View Answer

Answer: c
Explanation: The area of the segment = (\(\frac {x^{\circ }}{360^{\circ }}\) × πr2 ) – \(\frac {bh}{2}\)
= Area of the sector – Area of the triangle
= 44 – 12
= 32 m

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter