# Playing with Pencils

**Calculus**Level 5

Betsy is drawing with a mechanical pencil. She ends up drawing the closed figure shown above. All units are in

**inches**.This figure is given by the formula **sin(x)** from **0 to 2\(\pi \)**. Betsy desides to shade in the parts that are shaded in on the graph. She then decides to trace the outer ends of the figure with a thickness of **1/50** of an inch without lifting her pencil.

She uses ** 1** piece of graphite after drawing

**80.56 \(\text{inches} ^2 \)**. Let

*a*be the number of these figures (with the shaded and outlined areas) that she can draw with this

**piece of graphite. Find**

*1**a*+1.

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