Question

a water tank in the shape of a right circular cone has an altitude of 15 feet and a base radius of 10 feet. If the tank is full of water, find the work done in pumping all the water over the top of the tank.

Answer 1

For the purpose of SI units, I convert the foot to meter first

Altitude=15 feet=4.571meter

Radius at top=10feet=3.04m

Pouring out water is required from 0 to height of 4.571 full height of tank. It requires integration to be done on the given limit

Work = Force x distance

Force=weight density x volume

Force=9.81x density x volume

Force=9.81x1000xvolume

Force=9.81*1000*3.14* x^2*dy

Work=9.81*1000*3.14* x^2*dy(15-y)

Work=9.81*1000*3.14* x^2* (15-y)dy

Slope=m=15/10=1.5

y-0+m(x-0)

y=1.5x

x=y/1.5

x=2/3y=

Thus work is

Work=9.81*1000*3.14* (0.66^2)* (15-y)dy

Work=13690.4(15-y)dy

Work=13690.4(15y-y^2)

Work=13690.4(15*4.571-(4.571)^2))

Work=652634.49Nm