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 circular puddle is growing, we can use the formula for the area of a circle, A = πr². To find how fast the area is changing with respect to time (dA/dt), we can use implicit differentiation.

First, differentiate A with respect to time (t):

dA/dt = d/dr(πr²) * dr/dt = 2πr * dr/dt.

Given the radius ® is 6 inches and the rate of growth of the radius (dr/dt) is 0.3 inches/minute, we plug these values into the equation:

dA/dt = 2π(6 inches)(0.3 inches/minute).

This simplifies to:

dA/dt = 3.6π inches²/minute.

Now, applying the value of π:

dA/dt ≈ 11.3 inches²/minute (rounded to one decimal place).

So, the area of the puddle is growing at about 11.3 square inches per minute when the radius is 6 inches.