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?

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?

marigirl · Answer

I think:
We are to find out:
$$\frac{ dh }{ dt } $$

We know
$$\frac{ dV }{ dt }=350$$

marigirl · Answer

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marigirl · Answer

Volume of cone: $$V=\frac{ 1 }{ 3 }\pi r^2h$$

Volume of this cone:$$V=\frac{ 2500 }{ 3 }h$$

phi · Answer

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

phi · Answer

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