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

MATH 180 December 2017
Other MATH 180 Exams

### Question 08 (a)

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 ${\textstyle R}$ .

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