Question

The angle subtended at the centre of a circle of
radius 15 cm by an arc of length 15.7 cm is
(it = 3.14)
(A) 30°
(B) 45°
(C) 60°
(D) 90°
​

Answer 1

Step-by-step explanation:

hope this is helpful.....

Answer 2

The angle subtended at the centre of a circle of radius 15 cm by an arc of length 15.7 cm is → option (C): 60°.

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Let's understand a few concepts:

To calculate the angle subtended at the centre of the circle we will use the following formula:

$\boxed{\bold{Arc\:length = \frac{\theta}{360\°}\times 2\pi r }}$

where θ = angle subtended at the centre of the circle and r = radius of the circle

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Let's solve the given problem:

The radius of the circle (r) = 15 cm

The length of the arc of the circle = 15.7 cm

Let the angle subtended at the centre of the circle be "θ".

Therefore, by using the above formula, we can form an equation,

$15.7 = \frac{\theta}{360\°}\times 2\times 3.14\times 15$

$\implies 15.7 = \frac{\theta}{360\°}\times 94.2$

$\implies \theta = 15.7\times \frac{360}{94.2}$

$\implies \bold{\theta = 60\°}$ ← option (C)

Thus, the angle subtended at the centre of a circle of radius 15 cm by an arc of length 15.7 cm is 60°.

#SPJ3

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