Water is leaking out of an inverted conical tank at a rate of 10100 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 17 centimeters per minute when the height of the water is 3 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Water is leaking out of an inverted conical tank at a rate of 10100 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 17 centimeters per minute when the height of the water is 3 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Question
Water is leaking out of an inverted conical tank at a rate of 10100 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 14 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 17 centimeters per minute when the height of the water is 3 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Expert Solution
Step 1: Introduction to the Question
Given: From an inverted conical tank water is leaking out of at a rate of cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has heightmeters and the diameter at the top is meters. If the water level is rising at a rate of centimeters per minute when the height of the water is meters,
Aim: To find the rate at which water is being pumped into the tank in cubic centimeters per minute.
Approach: To solve this problem, related rates and the properties of similar triangles can be used.
Formula Used: The volume of a cone .
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