An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 /sec , how fast is the depth of the water dropping when the height is 5in?

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- March 19th 2010, 09:40 PMyoman360An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing o
An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 /sec , how fast is the depth of the water dropping when the height is 5in?

- March 19th 2010, 11:08 PMsa-ri-ga-ma
Volume of the cone V = 1/3*π*r^2*h.....(1)

You want to find dh/dt. So you have to find r in terms of h.

r and h are proportional tp R and H, where R = 21" and H = 15".

So R/H = r/h.

So r = (R/H)*h.

Substitute this value in the eq.(1) and find dV/dt.

dV/dt is given. Find dh/dt. - March 20th 2010, 03:14 PMyoman360
- March 20th 2010, 03:18 PMyoman360