To solve this problem we will apply the concepts related to the final volume of a body after undergoing a thermal expansion. To determine the temperature, we will use the given relationship as well as the theoretical value of the volumetric coefficient of thermal expansion of copper. This is, for example to the initial volume defined as 
, the relation with the final volume as
Initial temperature = 
Let T be the temperature after expanding by the formula of volume expansion
we have,
Where 
is the volume coefficient of copper 
Therefore the temperature is 53.06°C
<span>Assume: neglect of the collar dimensions.
Ď_h=(P*r)/t=(5*125)/8=78.125 MPa ,Ď_a=Ď_h/2=39 MPa
τ=(S*Q)/(I*b)=(40*〖10〗^3*π(〖0.125〗^2-〖0.117〗^2 )*121*〖10〗^(-3))/(π/2 (〖0.125〗^4-〖0.117〗^4 )*8*〖10〗^(-3) )=41.277 MPa
@ Point K:
Ď_z=(+M*c)/I=(40*0.6*121*〖10〗^(-3))/(8.914*〖10〗^(-5) )=32.6 MPa
Using Mohr Circle:
Ď_max=(Ď_h+Ď_a)/2+âš(Ď„^2+((Ď_h-Ď_a)/2)^2 )
Ď_max=104.2 MPa, Ď„_max=45.62 MPa</span>
The reason as to why the substage condenser does not need to be included in computing the magnification and the only component needed is the ocular lens and the objective lenses is because the condenser is only responsible for gathering light and it does not contribute with the magnification of the object under the microscope.
To determine the height of the object given the time, we simply use the given relation between height and time in the problem statement. It is given as:
h = -16t^2 + 127t
We substitute 55 seconds to t and obtain,
h = -16(55)^2 + 127(55)
h = - 41415
