Question

A water tank is in the shape of a right circular cone with height 18 ft and radius 12 ft at the top. If it is filled with water to a depth of 15 ft, find the work done in pumping all of the water over the top of the tank. Recall that the density of water is δ=62.4 lb/ft3.

Answer 1

661284 lb-ft

Step-by-step explanation:

We are given that height of water tank=18 ft

Radius of circular tank=12 ft

Density of water=
`62.4 lb/ft^3`

`(r)/(h)=(12)/(18)=(2)/(3)`

`r=(2)/(3)h`

We have to find the work done in pumping all of the water over the top of the tank.

`m=density* volume`

`W=m* distance=62.4* \pi r^2 (18-h) dh`

`W=62.4* 3.14* (4)/(9)h^2(18-h)dh`

`W=195.936\cdot \int_(0)^(15)(8h^2-\farc{4}{9}h^3dh`

`W=195.936* [(8h^3)/(3)-(h^4)/(9)]^(15)_0`

`W=195.936* 3375=661284 ftlb`

Hence, the work done in pumping all of the water over the top of the tank=661284 ft lb.