Answer
a). $I_{x}=22.5kg.m^{2}$,
b). $I_{y}=62.5kg.m^{2}$,
c). $I_{z}=85kg.m^{2}$.
Work Step by Step
a). $I_{x}=4\times1.5^{2}+3\times1.5^{2}+2\times1.5^{2}+1\times1.5^{2}=22.5 kg.m^{2}$
b). $I_{y}=4\times2.5^{2}+3\times2.5^{2}+2\times2.5^{2}+1\times2.5^{2}=62.5 kg.m^{2}$
c). $I_{z}=4\times(\frac{\sqrt 34}{2})^{2}+3\times(\frac{\sqrt 34}{2})^{2}+2\times(\frac{\sqrt 34}{2})^{2}+1\times(\frac{\sqrt 34}{2})^{2}=85 kg.m^{2}$
