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Liquid if flowing into a conical tank (with vertext down) that has a radius two times its height. If the height of the liquid increases at a rate of 5 feet per minute when the liquid is 9 feet high, find the rate at which the volume of liquid in the tank is increasing at this instant. Give exact answer.  V= pi/3 r2h

Liquid if flowing into a conical tank (with vertext down) that has a radius two times its height. If the height of the liquid increases at a rate of 5 feet per minute when the liquid is 9 feet high, find the rate at which the volume of liquid in the tank is increasing at this instant. Give exact answer.  V= pi/3 r2h

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Liquid if flowing into a conical tank (with vertext down) that has a radius two times its height. If the height of the liquid increases at a rate of 5 feet per minute when the liquid is 9 feet high, find the rate at which the volume of liquid in the tank is increasing at this instant. Give exact answer.  V= pi/3 r2h

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V=\frac{1}{3}\pi r^2h

a radius two times its height

so take r=2h

V=\frac{1}{3}\pi \left(2h\right)^2h

V= \frac{1}{3}\pi \cdot 4h^2h

V= \frac{4}{3}\pi h^3

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