Answer
2.24 m
Work Step by Step
Please see the attached image first.
We can write,
The probe's weight is W = 135 kg
The weight of the displaced hydrocarbon is $W_{h}=m_{h}g=\rho_{h}V_{sub}g$
By Archimedes' principle, $W_{h}$ is equal in magnitude to the buoyancy force, which balances gravity when the slab is in equilibrium. So,
$135g\space kg=482\space kg/m^{3}\times V\times g$
$0.28\space m^{3}=V$
Total volume of the probe $= 2V = 0.56\space m^{3}$
We can write the volume of a cylinder $(V) =\pi r^{2}h$
Let's plug known values into this equation,
$0.56\space m^{3}=\pi (\frac{0.563m}{2})^{2}h$
$2.24m=h$
