A brush fire is burning a circular area whose radius is increasing at a rate of 3 feet per minute. How fast is the area of the fire increasing when its radius is 25 feet?
A) $225 \pi \mathrm{ft} 2 / \mathrm{min}$
B) $625 \pi \mathrm{ft} 2 / \mathrm{min}$
C) $75 \pi \mathrm{ft}^{2} / \mathrm{min}$
D) $150 \pi \mathrm{ft} 2 / \mathrm{min}$

Question

Quizplus · Accepted Answer

The rate of change of the area $A$ of a circle with respect to time $t$ is given by $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$. Substituting $r = 25$ feet and $\frac{dr}{dt} = 3$ feet/min, we get $\frac{dA}{dt} = 2\pi \times 25 \times 3 = 150\pi$ square feet per minute.

A Brush Fire Is Burning a Circular Area Whose Radius 225πft2/min225 \pi \mathrm{ft} 2 / \mathrm{min}225πft2/min

A Brush Fire Is Burning a Circular Area Whose Radius $225 \pi \mathrm{ft} 2 / \mathrm{min}$