Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 08 (a)/Statement

Consider two tanks of water, one above the other, as pictured below. The top tank, which is initially full, is a cylinder of radius ${\textstyle R}$ and height ${\textstyle H}$. The bottom tank, which is initially empty, is a cone of radius ${\textstyle R}$ and identical volume as the top tank. Suppose water drains at a constant rate ${\textstyle C}$ from the top tank to the bottom tank.

(a) Find the rate at which the depth of water in the bottom tank is increasing when it is equal to ${\textstyle H}$. Your answer should be in terms of ${\textstyle C}$ and ${\textstyle R}$.