Mathematics Multiple Choice Questions & Answers 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
Answer: b
Clarification: 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
Answer: c
Clarification: 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
Answer: a
Clarification: 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.
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
Answer: b
Clarification: 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
Answer: d
Clarification: 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
Answer: c
Clarification: 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
Answer: b
Clarification: 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
Answer: a
Clarification: 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
Answer: a
Clarification: 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
Answer: c
Clarification: 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