We need to know about the rate of change to solve the problem. The rate of change of the volume of the cone is 16097.52 cubic in/s
The rate of change of a quantity is the rate at which it either increases or decreases. In this question we know that the radius is increasing at a rate of 1.3 in/s, height is decreasing at a rate of 2.1 in/s, we need to find the rate of change of volume given the radius is 122 in and the height is 147 in.
volume of a cone=[tex]\pi r^{2}[/tex]h/3
dV/dt=[tex]\pi[/tex]/3(2rh dr/dt+[tex]r^{2}[/tex] dh/dt)=[tex]\pi[/tex]/3(2x122x147x1.3 -122x122x2.1)=16097.52
Therefore the change in volume is 16097.52 cubic in/s.
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