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Question Number 213661 by Spillover last updated on 13/Nov/24

Commented by MathematicalUser2357 last updated on 14/Nov/24

Answered by mahdipoor last updated on 14/Nov/24

$$M\stackrel{-}{y}={\int }_{M}ydm\Rightarrow \rho =cte,dm=\rho dV$$$$V\stackrel{-}{y}={\int }_{V}ydV={\int }_0^{1}y\left(\pi z^{2}dy\right)=\pi {\int }_0^{1}y\left(\frac{y}{4}\right)dy=\frac{\pi }{12}$$$$V={\int }_0^1\left(\pi z^2\right)dy=\frac{\pi }{8}$$$$\Rightarrow \stackrel{-}{y}=\frac{\pi /12}{\pi /8}=\frac{2}{3}$$$$$$

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