Question

Rate of change -Differentiation
An inverted cone with a base area of 2500pi mm^2 and height of 300m is slowly being filled with water. Water is being poured in at a rate of 350 mm^3/s. At what rate is the height of the water changing when the water is 100mm from the top of the inverted cone?

Answer 1

I think:
We are to find out:
\[\frac{ dh }{ dt } \]

We know
\[\frac{ dV }{ dt }=350\]

Answer 2

Volume of cone: \[V=\frac{ 1 }{ 3 }\pi r^2h\]

Volume of this cone:\[V=\frac{ 2500 }{ 3 }h\]

Answer 3

use "similar triangles" to write r in terms of h

Answer 4

from the area of the base you find r=50
and you have this