Question

An oil tanker spills oil that spreads in a circular pattern whose radius increases at a rate of 15 ft/min. Let A be the area of the circle and r be the radius of the circle. How fast is the area increasing when the radius is 30 feet

Answer 1

Answer:

$2827.4 \dfrac{ft}{s}$

Step-by-step explanation:

$A = \pi r^2$

$\dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt}$

$\dfrac{dA}{dt} = 2 \times \pi \times 30~ft \times 15 \dfrac{ft}{s}$

$\dfrac{dA}{dt} = 2827.4 \dfrac{ft}{s}$