When the radius is 186 in. and the height is 148 in., the cone's volume decreases at rate 16,173 in³/s
Volume of a cone is given by:
V = 1/3. πr².h
Where:
r = base radius
h = height
Take the derivative with respect to t
dV/dt = 1/3 . π . (r².dh/dt + h. 2r. dr/dt)
Parameters given in the problem:
dr/dt = 1.6 in/s
dh/dt = -2.1 in/s
r = 186 in.
h = 148 in.
Plug the parameters into the derivative"
dV/dt = 1/3 . π . (186².(-2.1) + 148. 2. 186. 1.6)
dV/dt = 16,173 in³/s
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