Answer:
[tex]\Delta V = - 216.415 mm^3[/tex]
Step-by-step explanation:
we know that change is length is calculated by following strain relation
[tex]\Delta L = L \times \epsilon_x[/tex]
where strain is given as
[tex]\epsilon_x = \frac{\sigma_x - \nu(\sigma_y + \sigma_z)}{E}[/tex]
[tex]\epsilon_x = \frac{-10^8 - 0.35 ( -10^8 -10^8 (N/m^2))}{7.5 \times 10^10}[/tex]
[tex]\epsilon_x = -4.453 \times 10^{-4} [/tex]
plugging strain value in change in length formula
[tex]\Delta L = 90 \times -4.453 \times 10^{-4} = - 0.04008 mm[/tex]
calculate the length on the longer side
[tex]L_{long} = L = \delta L[/tex]
= 90 - 0.04008 = 89.95 mm
intial volume [tex] = 90*60*30 = 1.62 \times 10^5 mm^3[/tex]
change in volume
[tex]\Delta V =V ( \epsilon_x +\epsilon_y + \epsilon_z )[/tex]
[tex]\Delta V = 1.62 \times 10^5 (-4.453 - 4.453 - 4.453) \times 10^{-4}[/tex]
[tex]\Delta V = - 216.415 mm^3[/tex]
