The magnitude of the area of a circle is seven times that of its circumference. What is the circumference (in units) of the circle?

### Concept & Equation Set up a direct algebraic equation substituting the standard formulas for the area and circumference of a circle. $$\pi r^2 = 7 \times (2\pi r)$$ ### Step-by-Step Solution * Given: Area $= 7 \times$ Circumference. * Substitute the formulas: $\pi r^2 = 7 \times 2\pi r$. * Divide both sides by $\pi r$ (since $r > 0$): $r = 14$. * Now calculate the circumference using $r = 14$: $C = 2\pi r = 2 \times \frac{22}{7} \times 14$. $C = 2 \times 22 \times 2 = 88$. ### Exam Strategy & Shortcut Notice the cancellation: $\pi r^2 = k \times (2\pi r) \Rightarrow r = 2k$. Here, $k = 7$, so $r = 14$. The circumference is simply $2 \pi r = 2 \times \frac{22}{7} \times 14 = 88$. ### Common Pitfall A common mistake is finding the radius ($r = 14$) and stopping, but the question explicitly asks for the *circumference*. ### Final Answer Therefore, the correct answer is **88**.