A tank in the shape of an inverted right circular cone has height meters and radius meters. It is filled with meters of hot chocolate.

Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is

$\displaystyle

A = \pi r^2

$

$\displaystyle

V = \pi r^2 \triangle{x}

$

$\displaystyle

\frac{r}{h} = \frac{13}{8}

\frac {r}{8-x} = \frac{13}{8} r=\frac{13}{8}(8-x)

$

$\displaystyle

V = \pi (\frac{13}{8})^2 (8-x)^2 \triangle x

$

$\displaystyle

F = ma = V*p*g

$

$\displaystyle

F = \pi (\frac{13}{8})^2 (8-x)^2 (1550)(9.8) \triangle x

$

$\displaystyle

W = \int^8_1 [\pi (\frac{169}{64}) (8-x)^2 (1550)(9.8)] dx

$

$\displaystyle

W = \frac{2567110\pi}{64} \int^8_1 (8-x)^2 dx

$

$\displaystyle

W = 14407454.03 J

$

Can anyone see where i went wrong?

Thanks for any help