Questions: Find the radius of the circle in the figure to the right. The radius of the circle is □ (Type an integer or a simplified fraction.)

Solution Steps

The arc length is given as $7\pi$, and the central angle is given as $\frac{7\pi}{4}$.

The arc length ($s$) of a circle with radius $r$ and central angle $\theta$ (in radians) is given by the formula $s = r\theta$.

We have $s = 7\pi$ and $\theta = \frac{7\pi}{4}$. We can solve for the radius $r$ using the arc length formula: $7\pi = r \times \frac{7\pi}{4}$ Multiply both sides by $\frac{4}{7\pi}$: $7\pi \times \frac{4}{7\pi} = r \times \frac{7\pi}{4} \times \frac{4}{7\pi}$ $4 = r$

Final Answer: The radius of the circle is 4.