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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

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