Science:Math Exam Resources/Courses/MATH110/December 2014/Question 09 (b)/Statement

When a pebble is thrown into a pond, circular ripples form on the water surface. Suppose ${\textstyle r(t)}$ is the radius, in centimetres, of one such ripple at ${\textstyle t}$ minutes after the pebble falls into the water, and ${\textstyle A(r)}$ is the surface area of a ripple of radius ${\textstyle r}$.

(b) Suppose the radius of the ripple increases at a rate of 20 centimetres per minute. How fast is the area of the ripple increasing when the radius is 10 cm? Include units. (Recall the area of a circle of radius ${\textstyle r}$ is ${\textstyle A=\pi r^{2}}$.)