A conical tank with radius 4 ft and height 10 ft was initially full of water is being drained at the rate of (1/6)√h.Find the formula for the depth and the amount of water in the tank at any time 2.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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First we will find the volume of the tank.

The tank is a conic shape, then the volume of the cone is given by"

`V = (1/3) r^2 pi h `

`=> V = (1/3)* 4^2 pi 10`

`==> v = (1/3) 160 pi`

`==> V =(160pi)/3`

`` The tank drains `(1/6) `

`==> h(t) = h - (1/6)ht= 10 - (1/6)10 * t = 10 - (10t)/6 = 10- (5t)/3`

`==> h(t)= 10 - (5t)/3 ` such that t is the time.

`V(t)= v - V*(1/6)*t `

`V(t)= (160pi)/3 - (160pi)/3 (1/6) t`

`V(t)= (160pi)/3 -(80pit)/9`

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