Answer to Question #119916 in Math for Gianfranco

Question

I was curious about how this will work if something many feet like let's say 100ft tall how will you do the weight of it? Like if you 100ft tall or 300ft it doesn't matter how can weight be determined of the height.

Answer 1

In general it is impossible (or very difficult) to determine the dependence between the height of the body and its weight.

If the body has a uniform density $\rho$ (homogeneous body), mass $m$ and volume $V$ then

$$m=\rho\cdot V$$

If the volume $V$ is simultaneously the direct proportional function of height $h$ then

$$V(h)=k\cdot h$$

In this case we have that mass of the body $m$ is directly proportional to its height $h$

$$m=K\cdot h, where\ K=\rho\cdot k$$

Or

$${m_2 \over m_1}={h_2 \over h_1}$$

Suppose we know the shape of the homogeneous body with density $\rho$ and the area of its base. Then we can find the volume of the body as function of its height and find the mass of the body.

For example, cylinder has a base radius $r=constant.$ Then

$$Area\ of\ base=A=\pi\cdot r^2=constant$$

$$Volume=V(h)=\pi\cdot r^2\cdot h$$

$$mass=m(h)=(\rho\cdot \pi\cdot r^2)\cdot h$$

Substitute $h$ and determine $m.$