The radius of a circular puddle is growing at a rate of 2 cm/s. How fast is the area growing at the instant when it equals 20 cm²? A)32 cm²/s B)10 cm²/s C)251 cm²/s D)16 cm²/s E)18 cm²/s

Question

Quizplus · Accepted Answer

The area of a circle is given by $A = \pi r^2$. Differentiating both sides with respect to time ($t$) gives $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$. Given $\frac{dr}{dt} = 2 \, \text{cm/s}$ and $r = 20 \, \text{cm}$, substituting these values gives $\frac{dA}{dt} = 2\pi(20)(2) = 80\pi \, \text{cm}^2/\text{s}$, which is approximately 251 cm^2/s.

The Radius of a Circular Puddle Is Growing at a Rate