Question

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.

(Use π = 3.14 and $\sqrt{3}$= 1.73)

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Answer 1

Answer:

Step-by-step explanation:

Solution:

In a circle with radius r and the angle at the centre of degree measure θ,

(i) Area of the sector = θ/360 × πr2

(ii) Area of the segment = Area of the sector - Area of the corresponding triangle

Let's draw a figure to visualize the area to be calculated.

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.

Here, radius, r = 15 cm, θ = 60°

Visually it’s clear from the figure that,

AB is the chord that subtends 60° angle at the centre.

(i) Area of minor segment APB = Area of sector OAPB - Area of ΔAOB

(ii) Area of major segment AQB = πr2 - Area of minor segment APB

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)

Here, Rradius, r = 15 cm, θ = 60°

Area of the sector OAPB = θ/360° × πr2

= 60°/360° × 3.14 × 15 × 15 cm2

= 117.75 cm2

In ΔAOB,

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)

OA = OB = r (radii of the circle)

∠OBA = ∠OAB (Angles opposite to the equal sides in a triangle are equal)

∠AOB + ∠OBA + ∠OAB = 180° (Angle sum property of a triangle)

60° + ∠OAB + ∠OAB = 180°

2 ∠OAB = 120°

∠OAB = 60°

∴ ΔAOB is an equilateral triangle because all its angles are equal.

⇒ AB = OA = OB = r

Area of ΔAOB = √3/4 × (side)2

= √3/4 r2

= √3/4 × (15 cm)2

= 1.73/4 × 225 cm2

= 97.3125 cm2

(i) Area of minor segment APB = Area of sector OAPB - Area of ΔAOB

= 117.75 cm2 - 97.3125 cm2

= 20.4375 cm2

(ii) Area of the major segment AQB = Area of the circle - Area of minor segment APB

= π × (15 cm)2 - 20.4375 cm2

= 3.14 × 225 cm2 - 20.4375 cm2

= 706.5 cm2 - 20.4375 cm2

= 686.0625 cm2

Answer 2

Step-by-step explanation:

Given :

radius=15cm, angle = 60°

find = Area of the corresponding minor and major segment of the circle.

solutions:

Area ( minor segment )

= area ( sector OAB ) - area ( triangle OAB )

= 0/360° πr^2 - √3/4 r^2

= 60/360 × 3.14×15^2 - 1:75/4 × 15^2

= 117.75 - 97.3125 = 20.4375 cm^2

Area of major segment = Area of circle - Area of minor segment.

= π^r2 - 20.4375

= 3.14 × 15^2 - 20.4375 = 686.06256m^2

Answer:

hence, area of minor segment = 20.4375 cm^2

area of major segment = 686.0625 cm^2