Question

An inverted pyramid is being filled with water at a constant rate of 70 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 11 cm. Find the rate at which the water level is rising when the water level is 7 cm

Answer 1

0.98 cm/s

Explanation:

We are given that

Height of pyramid=h=11 cm

Length of pyramid=Width of pyramid=l=b=4 cm

`(dV)/(dt)=70 cm^3/s`

We have to find the rate at which the water level is rising when the water level is 7 cm.

`(l)/(h)=(4)/(11)`

`l=(4)/(11) h`

Volume of pyramid=
`V=(lbh)/(3)=(l^2h)/(3)=(4^2h^3)/(33)=(16)/(33)h^3`

`(dV)/(dt)=(16)/(33)(3h^2)(dh)/(dt)`

`70=(16)/(33)(3* 7^2)(dh)/(dt)`

`(dh)/(dt)=(70* 33)/(16* 3* 7^2)`

`(dh)/(dt)=0.98 cm/s`