Question

sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. suppose the height of the pile infcreases at a rate of 1cm/s when the pile is 12 cm hight. at what rate is the sand leaving the bin at that instant

Answer 1

`(dv)/(dt) =7239.168 cm/sec`

Explanation:

From the question we are told that:

Rate
`(dh)/(dt)=1cm`

Height
`h=12cm`

Radius
`r=4h`

Generally the equation for Volume of Cone is mathematically given by

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

`V=(1)/(3)\pi (4h)^2h`

Differentiating

`(dv)/(dt) =(16)/(3)\pi3h^2(dh)/(dt)`

`(dv)/(dt) =(16)/(3)*3.142*3*12^2*1`

`(dv)/(dt) =7239.168 cm/sec`