# Pre-calculas

A conical tank of radius R=19 feet and height of H=16 feet is being filled with water at a rate of 9ft 3 /min .

(a) Express the height h of the water in the tank, in feet, as a function of time t in minutes

1. 👍 0
2. 👎 0
3. 👁 411
1. assuming the tank is pointed-end down, the water forms a cone, so

v = π/3 r^2 h

Now, using similar triangles, (r/h) = 9/16, so

v = (π/3)(9/16 h)^2 h = 27π/256 h^3
h = 3/8 ∛(2πv)

since this is precal, not calculus, I'm not sure what tools you have available to convert that to a function of time

1. 👍 0
2. 👎 0
2. Is the point at the bottom or the top?

whichever way you draw it
Volume of a cone = (1/3)pi R^2 x
where r is the radius of the surface and x is distance from the tip
r/x = 9.5/ 16 = .594
so
r = .594 x

v = (1/3) pi (.594x)^2 x
v = .369 x^3
dv/dx = 1.11 x^2
dv/dt = 1.11 x^2 dx/dt

but dv/dt = 9 ft^3/min
x^2 dx/dt = 9/1.11 = 8.11
x^2 dx = 8.11 dt
(1/3) x^3 = 8.11 t
x^3 = 24.3 t
x = (24.3 t)^(1/3)

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math - calc

A conical water tank with vertex down has a radius of 12 feet at the top and is 26 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 12

2. ### Math

A conical water tank with vertex down has a radius of 10 feet at the top and is 22 feet high. If water flows into the tank at a rate of 30 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 14

3. ### calculus

A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

4. ### Solid Mensuration

A closed cylindrical container 10 feet in height and 4 feet in diameter contains water with depth of 3 feet and 5 inches. What would be the level of the water when the tank is lying in horizontal position?

1. ### math

A conical water tank with vertex down has a radius of 13 feet at the top and is 28 feet high. If water flows into the tank at a rate of 10 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17

2. ### Calculus

Water is running into an open conical tank at the rate of 9 cubic feet per minute. The tank is standing inverted, and has a height of 10 feet and a base diameter of 10 feet. At what rate is the radius of the water in the tank

3. ### cal

A conical tank (with vertex down) is 12 feet across the top and 18 feet deep. If water is flowing into the tank at a rate of 18 cubic feet per minute, find the rate of change of the depth of the water when the water is 10 feet

4. ### Math

A fuel oil tank is an upright cylinder, buried so that its circular top 12 feet beneath ground level. The tank has a radius of 6 feet and is 18 feet high, although the current oil level is only 13 feet deep. Calculate the work

1. ### Math

The base of a pyramid-shaped tank is a square with sides of length 12 feet, and the vertex of the pyramid is 10 feet above the base. The tank is filled to a depth of 4 feet, and water is flowing into the tank at the rate of 2

2. ### calculus

1. A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at

3. ### college algebra

A propane tank has the shape of a circular cylinder with a hemisphere at each end. The cylinder is 6 feet long and volume of the tank is 5pie cubic feet. Find, to the nearest thousandth of a foot the length of the radius x.

4. ### Please check my calculus

A conical tank has a height that is always 3 times its radius. If water is leaving the tank at the rate of 50 cubic feet per minute, how fast if the water level falling in feet per minute when the water is 3 feet high? Volume of a