Test 4, Section 4, Number 36 (Calculator Section)

Great question. Remember that arc length and central angle are related thusly:

    \begin{align*}\dfrac{\text{central angle}}{360^\circ}=\dfrac{\text{arc length}}{\text{circumference}}\end{align*}

You have a circle with radius 10, so its circumference is 2\pi r=20\pi, or about 62.83. If the arc formed by the central angle has a length between 5 and 6, that means it’s between \dfrac{5}{62.83} and \dfrac{6}{62.83} of the full circumference.



Therefore, x can be any integer between 28.65 and 34.38: 29, 30, 31, 32, 33, or 34.

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