Respuesta :
The moment of inertia of the tetrahedron will be 435.75,Moment of inertia is found by the application of integration.
What is a moment of inertia?
The sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation expresses a body's tendency to resist angular acceleration.
The moment of inertia of a tetrahedron of constant density is found as;
[tex]\rm I_Z = \int\limits^a_b {dz} \, dv \\\\ dv=dxdy\\\\ I_Z = \int_0^9 \int_0^{8-\frac{8x}{9}} \int_0^{5-\frac{5x}{9} -\frac{5x}{8} }(x^2+y^2)dzdy[/tex]
After applying the limit, we get the answer is;
[tex]\rm I_Z= \frac{1743}{4} \\\\ I_Z= 435.75[/tex]
Hence, the moment of inertia of tetrahedron will be 435.75
To learn more about the moment of inertia, refer to the link;
https://brainly.com/question/15246709
#SPJ4
