The radius of a circular puddle of water is growing at a rate of 0.3 inches per minute. Find the rate at which the area of the puddle is growing when the radius of the puddle is 6 inches. (Round your answer to one decimal place.)

To find the rate at which the area of the puddle is growing, we'll use calculus related to the area of a circle. 1. **Area of a Circle:** \[ A = \pi r^2 \] 2. **Differentiate with respect to time (t):** \[ \frac{dA}{dt} = 2\pi r \frac{dr}{dt} \] 3. **Given Values:** - \(\frac{dr}{dt} = 0.3\) inches per minute - Radius \(r = 6\) inches 4. **Plug in the values:** \[ \frac{dA}{dt} = 2 \pi \times 6 \times 0.3 = 3.6\pi \] 5. **Calculate the numerical value:** \[ 3.6\pi \approx 3.6 \times 3.1416 \approx 11.3097 \text{ square inches per minute} \] 6. **Round to one decimal place:** \[ \frac{dA}{dt} \approx 11.3 \text{ square inches per minute} \] **Answer:** The area is increasing at approximately 11.3 in² per minute.