Question

(1) Find the length of an arc of a circle
which subtends an angle of 108° at the
centre, if the radius of the circle is 15
cm.​

Answer 1

$\LARGE{\underline{\sf{\blue{Solution:}}}}$

We have to find the length of the arc of a circle whose radius and subtends an particular angle at the centre.

Provided:

• Angle subtended by the arc = 108°
• Radius of the circle = 15 cm

We have to find the length of the arc for which we will use the appropriate formula.

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Formula for finding the length of arc:

$\large{ \because{ \boxed{ \sf{ \frac{ \theta}{360 \degree} \times 2\pi r}}}}$

Here, theta is the required angle subtended at the centre and r is the radius of the circle.

Plugging the given values of $\theta$ and r:

$\sf{ = \dfrac{108 \degree}{360 \degree} \times 2 \times \dfrac{22}{7} \times 15}$

$\sf{ = \dfrac{3 \times 2 \times 22 \times 15}{10 \times 7} }$

Simplifying further,

$\sf{ = \dfrac{ 22 \times 3 \times 3}{7}}$

$\sf{ \approx 28.28\:c m}$

Thus, our required length of the arc is 28.28 cm (Answer)

Answer 2

Answer:

Step-by-step explanation:

Given information: subtends angle at the center 108° and radius of the circle is 15 cm.

Formula for length of arc is

where, r is radius of the circle and θ is the subtends angle at the center.

The length of acr is

Therefore the length of arc is 28.275 cm.