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2 years ago

A circle has a radius of 48 millimeters. What is the central angle in radians, that intercepts an arc of length 36π millimeters?

Mathematics

2 answers:

Liono4ka [1.6K]2 years ago

8 0

Arc length= radius x angle
36pie=48 x angle
divide both side by 48
you get 3/4pie

Sphinxa [80]2 years ago

6 0

Answer:

$\theta=\dfrac{3\pi}{4}$

Step-by-step explanation:

The formula for length of intercepted arc is

$s=r\theta$

where, r is the radius of the circle and θ in the central angle in radian.

Radius of the circle = 48 millimeters

Length of intercepted arc = 36π millimeters

Substitute the given values in the above formula.

$36\pi=48\theta$

Divide both sides by 48.

$\dfrac{36\pi}{48}=\dfrac{48\theta}{48}$

$\dfrac{3\pi}{4}=\theta$

Therefore, the measure of central angle is $\theta=\dfrac{3\pi}{4}$ .

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