Question

An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 4 cm, and the height is 12 cm. Find the rate at which the water level is rising when the water level is 4 cm.

Answer 1

`(225)/(16) cm/s`

Explanation:

We are given that

`(dV)/(dt)=25cm^3/s`

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=
`(1)/(3)lwh=(1)/(3)l^2h`

`(l)/(h)=(4)/(12)=(1)/(3)`

`l=(1)/(3)h`

Substitute the value

`V=(1)/(27)h^3`

Differentiate w.r.t t

`(dV)/(dt)=(3)/(27)h^2(dh)/(dt)`

Substitute the values

`25=(1)/(9)(4^2)(dh)/(dt)`

`(dh)/(dt)=(25* 9)/(16)=(225)/(16) cm/s`