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The radius of a circle is 7.2 cm. If a central angle measures 112°, what is the length of its intercepted arc to the nearest hundredth?

Respuesta :

AL2006

-- The full central angle of the whole circle is 360° .

-- 112° is  (112/360) = 0.3111... of the whole circle.

-- If we can find the full circumference, then the arc inside
the 112° angle is just 0.3111 of the whole thing.

The circumference of a circle is  (pi) x (diameter).

The radius of this circle is  7.2 cm, so the diameter is 14.4 cm.

       Circumference = (pi) x (14.4 cm) = 45.239 cm

The arc inside the 112° angle is

                (0.3111...) x (45.239 cm)  =  14.074 cm

    Rounded to the nearest hundredth:  14.07 cm .

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