Question

A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.


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Answer 1

Answer:

• Area of minor segment 56 cm²
• Area of Major Segment 560 cm².

Step-by-step explanation:

According to the Question

It is given that chord of a circle of radius 14 cm makes a right angle at the centre.

we have to calculate the area of minor and major segment of the circle .

Firstly we calculate the area of minor segment .

From the above figure observe that

❒ Area of Minor Segment = Area of sector - Area of triangle

↠Area of Minor Segment = ∅/360 × πr² - 1/2×14 × 14

↠ Area of Minor Segment = 90/360 × 22/7 (14)² - 7×14

↠Area of Minor Segment = 1/4 × 22/7 × 196 - 98

↠Area of Minor Segment = 22×7 - 98

↠Area of Minor Segment = 154 - 98

↠Area of Minor Segment = 56cm²

• Hence, the area of minor segment is 56 cm²

Now calculating the Area of Major segment

❒ Area of Major Segment = Area of Circle - Area of Minor Segment

↠Area of Major Segment = πr² - 56

↠Area of Major Segment = 22/7 × 196 -56

↠Area of Major Segment = 22×28 - 56

↠Area of Major Segment = 616 - 56

↠ Area of Major Segment = 560 cm²

• Hence, the area of major segment is 560 cm².

Answer 2

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$Given radius(r)=14cm$

$⇒  Area of sector OABO= \frac{0}{360} \pi {r}^{2}$

$∴  Area of sector OABO= \frac{90}{360} \times \frac{22}{7} \times (14) {}^{2} = 154cm {}^{2}$

$⇒  Area of right angled △OAB= \frac{1}{2} \times 14 \times 14 = 98cm {}^{2}$

$∴  Area \: of \: the \: minor \: segment \: of \: the \: \\ circle  \: = \:  Area \: of \: sector  \: OABO \:  - \: Area \: of \: righta \: angled  \: △ABO$

$∴  Area \: of \: the \: minor \: segment \: of the$

circle =(154−98)cm2=56cm2

$circle =( \frac{154}{98} )cm = 56cm$

$⇒  Area of circle =πr2=722×14×14=616cm2$

$⇒  Area \: of \: the \: major \: segment \: of \: the circle$

$= Area \: of \: circle \: - Area \: of \: minor \: segment.$

$∴  Area \: of \: the \: major \: segment \: of the circle  \\ =(616−56)cm2=560cm2$