Double check my Work problem.

A water storage tank has the shape of an inverted right circular cone with a height of 20 feet and diameter of 20 feet.

How much work is needed to pump the water out of the tank 10 feet above the top of the tank.

Density of water is 62.4 lb/ft^3

So here is my work for the problem:

By similar triangles:

r/x = 10/20 => r=x/2

h=20-x

V = Integral of pi*r^2*h dx

V = Integral (0,10) of pi*(x/2)^2*(20-x) dx

V = pi*Integral (0,10) of 5x^2 - x^3/4 dx

V = pi[5x^3/3 - x^4/16] (0,10)

and solve. I'm mainly worried about my points of integration is 0,10 right?