Rate of change If a hemisphere bowl of radius 6 cm contains water to a depth of x cm,the volume of the water is Tx (18–x). Water is poured into the bowlat a rate of 3 cm³s-1. Find the rate at which the water level is rising whenthe depth is 2 cm.

This question is related to application of derivatives.

If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx (18-x). Water is poured into the bowl 3 at a rate of 3 cm³s-1. Find the rate at which the water level is rising when the depth is 2 cm.

If a hemisphere bowl of radius 6 cm contains water to a depth of x cm, the volume of the water is rx (18-x). Water is poured into the bowl 3 at a rate of 3 cm³s-1. Find the rate at which the water level is rising when the depth is 2 cm.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter8: Areas Of Polygons And Circles

Section8.5: More Area Relationships In The Circle

Problem 42E: A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft...

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Question

Rate of change

If a hemisphere bowl of radius 6 cm contains water to a depth of x cm,
the volume of the water is Tx (18–x). Water is poured into the bowl
at a rate of 3 cm³s-1. Find the rate at which the water level is rising when
the depth is 2 cm.

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