Question

A CENTRAL ANGLE OF 45 DEGREES SUBTENDS AN ARC OF 12 CM. WHAT IS THE RADIUS OF THE CIRCLE? Include solution. ​

Answer 1

Given:

A CENTRAL ANGLE OF 45 DEGREES SUBTENDS AN ARC OF 12 CM. WHAT IS THE RADIUS OF THE CIRCLE?

To find:

WHAT IS THE RADIUS OF THE CIRCLE?

Solution:

Let "r" be the radius of the circle.

The degree measure of an arc length or central angle, θ = 45°

The length of the arc = 12 cm

We know,

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

Now, on substituting the given values in the above formula of arc length, we get

$12 = \frac{45\°}{360\°}\times 2\times \frac{22}{7} \times r }}}$

$\implies 12 = \frac{1}{8}\times 2\times \frac{22}{7} \times r$

$\implies r = \frac{12\times 8 \times 7}{2 \times 22}$

$\implies r = \frac{672}{44}$

$\implies\bold{ r = 15.27\:cm}$

Thus, the radius of the circle is → 15.27 cm.

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