contestada

A conical tank is 8 meters high. The radius of the top is 2 meters. At what rate is the water running out if the depth is 3 meters and is decreasing at the rate of 0.4 meters per minute

Respuesta :

Answer:

DV/dt    = 0,2355 m³/min

Step-by-step explanation:

Conical tank volume    V  =  1/3 *π*r²*h

r radius at the top    2 meters

when depth of water is 3 meters the radius of the level of water is:

let     α  angle of vertex of cone then

tan∠α   = 2/8        tan∠α   = 1/4         tan∠α  = 0,25

At the same time when water is at 3 meters depth  radius is

tan∠α  = r/3             0,25*3= r         r  = 0,75 m

Now

DV/dt    =  (1/3)*π*r²*Dh/dt            

Dh/dt  =  0,4 meters/min

By substitution

DV/dt    = 0,2355 m³/min