Mathematics, 26.03.2021 05:40 sjackson0625p8w1a0
The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasing at a rate of 2.2 in/s. At what rate is the volume of the cone changing when the radius is 134 in. and the height is 136 in.
Answers: 3
.
in/s while its height is decreasing at a rate of 
in/s. 
in. and the height is 
in.
, 
, 
, 
be the volume of the cone.
.![\frac{dv}{dt} =\frac{1}{3}\pi \left [ r^2\frac{dh}{dt}+h\left ( 2r \right )\frac{dr}{dt} \right ]](/tpl/images/1222/5454/e2ccf.png)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ \left ( 134 \right )^2\left ( -2.2 \right )+\left ( 136\right )\left ( 2 \right )\left ( 134 \right )\left ( 1.9 \right ) \right ]](/tpl/images/1222/5454/cd14f.png)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ -39503.2+69251.2 \right ]](/tpl/images/1222/5454/708d6.png)
![\frac{dv}{dt} =\frac{1}{3}\pi\left [ 29748 \right ]](/tpl/images/1222/5454/ce2b9.png)
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The radius of a right circular cone is increasing at a rate of 1.9 in/s while its height is decreasi...
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