An inverted cone has a height of 15 mm and a radius of 16mm. The volume of the inverted cone is decreasing a rate of 534 cubic mm per second, with the height begin held constant. What is the rate of change of the radius, in mm per second, when the radius is 6 mm? Round your answer to the nearest hundreth. (Do not include any units in your answer Remember that the volume of a cone is =V=13πr2h

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An inverted cone has a height of 15 mm and a radius of 16mm. The volume of the inverted cone is decreasing a rate of 534 cubic mm per second, with the height begin held constant. What is the rate of change of the radius, in mm per second, when the radius is 6 mm?   Round your answer to the nearest hundreth. (Do not include any units in your answer  Remember that the volume of a cone is =V=13πr2h

Tamara Donohue · Accepted Answer

Step 1   The volume of a cone is=V=13πr2h  The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height begin held constant.  =dVdt=13/πh.dr2dt as h is held constant and hence =dhdt=0  Step 2  Find the formula for the rate of change of the volume, in mm per second.   =dVdt=13πhddt(r2)  =13πh(2r)ddt(r)  =23πrhddt(r)  Step 3  To find the rate of changt of the radius, in mm per second, when the radius is 6 mm.  Here =dVdt=534 cubic mm per second, =h=15mm and =r=6mm.  =drdt=23πrhddt(r)  =⇒drdt=32πrhdVdt(r)  =32π×6×15×534  =2.8329

An inverted cone has a height of 15 mm and a radius of 16mm. The volum

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