Question

a chord of circle of radius 14 cm makes a right angle with at at the centre calculate the area of minor segment of the circle the area of major segment of a circle

Answer 1

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.

Answer 2

a chord of circle of radius 14 cm makes a right angle with at at the centre calculate the area of minor segment of the circle the area of major segment of a circle

Chord with circle center point will make equilateral right angled triangle which has equal sides = radius

let say chord = AB

then triangle = OAB

there will be one arc segment OAB

area of minor segment =Area of Arc segment OAB - Area of Triangle OAB

formula for segment area of circle =

$( \frac{segment \: angle}{360} ) \times \pi \times {radius}^{2}$

segment angle = 90 deg

radius = 14 cm

$\pi = \frac{22}{7}$

Area of Arc segment OAB = (90/360)×(22/7)×14×14 = 154 cm^2

Area of triangle OAB = (1/2) × 14 ×14 = 98 cm^2

Area of minor segment = 154 - 98 = 56 cm^2

Area of major segment = area of circle - Area of minor sement

= (22/7)×14×14 - 56

= 616 - 56

= 560 cm^2

minor segment area = 56 cm^2

major segment area = 560 cm^2