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

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

View Answer

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) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^{2}

b) \(\frac {x^{\circ }}{360^{\circ }}\) + πr^{2}

c) \(\frac {x^{\circ }}{360^{\circ }}\) – πr^{2}

d) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^{3}

View Answer

Explanation: The area of the sector is \(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}

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

View Answer

Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}

= \(\frac {50^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 5

^{2}

= 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

Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}

= \(\frac {134^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 12

^{2}

= 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

View Answer

Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}

= \(\frac {123^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 138

^{2}

= 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

Explanation: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}

= \(\frac {70^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 6

^{2}

= 21.99 m

8. Number of sectors in a circle are ____

a) 2

b) 3

c) 4

d) 1

View Answer

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

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

View Answer

Explanation: The area of the segment = (\(\frac {x^{\circ }}{360^{\circ }}\) × πr

^{2}) – \(\frac {bh}{2}\)

= Area of the sector – Area of the triangle

= 44 – 12

= 32 m

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

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