# Math Help - Calculate the work against gravity..?

1. ## Calculate the work against gravity..?

Calculate the work against gravity required to build a tower of height 35 ft in the shape of a right circular cone with base of radius 7 ft out of brick. Assume that brick has density .

___________ ft-lbs.

2. Originally Posted by tbenne3
Calculate the work against gravity required to build a tower of height 35 ft in the shape of a right circular cone with base of radius 7 ft out of brick. Assume that brick has density .

___________ ft-lbs.
The work required to raise a mass $m$ to a height $h$ is $w=mgh$.

The radius of the cone at a height $0\le h\le 35$ feet is:

$r=-\frac{h}{5}+7$

The volume of a slice of the cone perpendicular to the axis at a height $h$ and of thickness $\Delta h$ is:

$V_{\Delta h}(h)=\pi r^2 \Delta h=\pi (7-(h/5))^2 \Delta h$

Now the work can be seen to be:

$\int_{h=0}^{35} \pi r^2 \rho\, g\, h \; dh=\int_{h=0}^{35}\pi (7-(h/5))^2 \rho\, g\, h \; dh$

CB