A chord of radius 14cm makes centre angle of 90° then find the minor and major segments .
Answers
Answer:
Area of the small segment.(Green Area) = 56 Square cm.
Area of the big segment = 260 Square cm.
Step-by-step explanation:
Please see the attached diagram for the problem description.
We need to measure the green colored area for small segment.
The remaining area in circle is area of bigger segment.
AB is the Chord. Radii drawn from points A & B are making 90 degrees at the center of the circle.
Thus ∆AOB is a right angl triangle with height and base both equal to radius ‘r’. = 14 cm
Area of the small segment.(Green Area) = Total are covered by sector AoB – Area of the triangle AOB.
Area of the sector AOB = (ᶿ/360) ∏*r^2
Since ᶿ = 90
Area of the sector AOB = (90/360) 22*14*14/7 = 154 Square cm
Area of the Triangle AOB = height * base / 2 = 14 * 14 / 2 = 98 Square cm.
Area of the small segment.(Green Area) = 154 – 98 = 56 Square cm.
Area of the big segment = Area of the circle - Area of the small segment.(Green Area)
= 22*14*14/7 – 56 = 316 – 56 = 260 Square cm
