1. **State the problem:** We need to find how fast the area of an oil spill is increasing when the radius is 26 m, given the radius increases at 2 m/s. 2. **Formula used:** The area $A$ of a circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Differentiate with respect to time $t$:** To find the rate of change of area, differentiate both sides: $$\frac{dA}{dt} = \frac{d}{dt}(\pi r^2) = 2\pi r \frac{dr}{dt}$$ 4. **Given values:** - $\frac{dr}{dt} = 2$ m/s (rate of radius increase) - $r = 26$ m (radius at the instant) 5. **Substitute values:** $$\frac{dA}{dt} = 2\pi \times 26 \times 2 = 104\pi$$ 6. **Final answer:** The area is increasing at a rate of $$104\pi \approx 326.73$$ m$^2$/s when the radius is 26 m.