Question

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

This question was addressed to me during an online exam.

My doubt is from Area of Sector and Segment of a Circle topic in portion Area Related to Circles of Mathematics – Class 10

Answer 1

Right choice is (c) 40882.8 m

To elaborate: 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