Pre-Calculus...?

Question

Water is flowing at a rate of 5 meters cubed per second into the conical tank shown at the right. (the conical tank is an upsidedown cone that has a diamater of 60 meters and a height of 120 m. and then there's water filled into it and the height is "h", and it doesn't tell you the radius. )
a. Find the volume "V" of the water as a function of the water level "h".
the answer in the back of the book says: [(pi)(h cubed)] over 48.
but i got [(pi)(h cubed)] over 12.

please help.
thank youu!! :)

Answer 1

Andy S made a mistake at the end.. let me tell u from the begining.
_____-_30m_-
\.........|........./
.\........|......../
..\.120|---r--/
...\......|....../
....\.....|...../
.....\....|.h./
......\...|.../
.......\..|../
........\.|./
.........\|/
120 is the total height. 30 m is the half radius r is the half radius of the water cilinder. and h is the height of water. The quest. is asking for the volume of the water right. Volume of a cilinder is π*r²*h/3. what we have to do is to write r in h format. for doing this we will use similarity in triangles. r/h = 30/120 then u will find that r = h/4. when we put this equality in our Volume formula. we will find out V = π*(h/4)²*h/3.
V = π*h²/16*h/3
V = π*h³/48

I hope the shape will be helpfull and the answer will be chosen as the best

Answer 2

At any level of water in the tank, the relationship between h and r is given by

h/r = 120/30 = 4,

r = h/4

volume = pi r^2 h / 3 = pi h^3/48

Answer 3

The ratio of the diameter to the height of the cone will remained fixed up and down the cone..

Call d the diameter of the cone at height h
60/120 = d/h so d = h/2 and r = d/2 = h/4

The volume of a cone is pi*r^2*h/3..
V(h) = pi*(h/4)^2*(h/3) = pi*h^2/48

Thanks saruhanu. Ooooopsy, sorry :-)
<> pi*h^2/48 = pi*h^3/48

Answer 4

This can be a Cal question, take the derivative.

Answer 5

go to www.cramster.com; if you go there you can get step by step solutions to the problem if you have an American Textbook.