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ACT® Math

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Circumference and Perimeter

ACTMAT-JY7JVL

A belt (indicated in red in the figure below) is wrapped around two circular wheels.

The wheel represented by circle O has a diameter of 24 feet and the wheel represented by circle P has a diameter of 6 feet. The straight parts of the belt (represented by $ \overline{AB} $ and $ \overline{DC} $) are tangent to the wheels at points A, B, C, and D.

If the belt is wrapped around$\frac{2}{3}$ of the larger wheel (circle O) and wrapped around $\frac{1}{3}$ of the smaller wheel (circle P), how long is the belt (in feet)?

A

$ 6(3\pi + 10) $

B

$ 30(\pi+ 1) $

C

$ 18 (\pi + 2) $

D

$ 9 (2\pi + {\sqrt { 3 } }) $

E

$ 18 (\pi + {\sqrt { 3 } }) $