2016 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

The circumference of a circle is $100\pi \text{cm}$ . What is the radius of the circle?

$\textbf{(A)}\ 20 \text {cm} \qquad\textbf{(B)}\ 100 \text {cm} \qquad\textbf{(C)}\ 50 \text {cm} \qquad\textbf{(D)}\ 25 \text {cm} \qquad\textbf{(E)}\ 10 \text {cm}$

Solution

Let $r$ be the radius of the circle. Using the equation for the circumference of a circle, we have:

$2\pi r = C = 100\pi$

$r = \frac{100\pi}{2\pi} = \boxed {\textbf {(C) } 50 \text {cm}}$

~anabel.disher

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2016 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

Solution