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miv72 [106K]
2 years ago
11

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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