The volume of a right circular cylinder with radius r and height h is Vrh. Is the volume an increasing or decreasing function of
the radius at a fixed height%E2%80%8B (assume r0 and h%E2%80%8B0)?
1 answer:
Answer:
The rate of change of volume of the cone with respect to radius is
.
Step-by-step explanation:
radius of come = r
height of cone = h
Volume of cone
![V = \frac{1}{3}\pi\times r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%20r%5E2%20h)
As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.
![\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh\\\\](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdr%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%20%7B2r%7Dh%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdr%7D%3D%5Cfrac%7B2%7D%7B3%7D%5Cpi%5Ctimes%20rh%5C%5C%5C%5C)
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