Answer to Question #287294 in Mechanical Engineering for george2000

Question

A metal cube(faces 20 mm+-0.1mm) fully sinks into a glass full of water. The diameter of the glass is 60 mm+-0,2 mm.Calculate the water rise level and its cumulative error.

Answer 1

The water rise level:

$$\Delta h=V_\text{cube}/A_\text{glass},\\\space\\ \Delta h=a^3/(\pi d^2/4)=\dfrac{4a^3}{\pi d^2}=2.8\text{ mm}.$$

The cumulative error: 0.1+0.2=0.3 mm.