A circular plot of land is divided into two regions by a chord of length 10√3 meters such that the chord subtends an angle of 120∘ at the center. Then, the area, in square meters, of the smaller region is
Started 2 hours ago by Admin in
Explanatory Answer
Solution:
Given:
OA = OB = radius (r)
∠AOB = 120°
⇒ ∠OAB = ∠OBA = 30°
Consider OM ⟂ AB.
In right △OMB:
cos30° = MB / OB = (√3)/2 = (5√3)/OB
⇒ OB = 10
Also,
sin30° = OM / OB = 1/2 = OM / 10
⇒ OM = 5
Now, area of smaller region =
Area of sector − Area of △AOB
= (120/360) × π × (10)^2 − (1/2) × (10√3) × 5
= (1/3) × 100π − 25√3
= 25(4π/3 − √3)
Answer:
25(4π/3 − √3)
-
No one is replied to this question yet. Be first to reply!
Previous year papers
2024
2023
2022
2021
2020
2019
2018