# 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

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.

2. What is the name of the sector with a smaller area?
a) Small
b) Narrow
c) Minor
d) Tiny

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

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

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

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

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

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

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

8. Number of sectors in a circle are ____
a) 2
b) 3
c) 4
d) 1

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

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.

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

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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