Question

1

Answer: X = 244 mm Y = 117.7 mm

Answer 1

Figure "1" is a rectangle. Figure "3" is a triangle. Figure "2" is a circle.

$$ \begin{array}{c|cc|c} \text { Figure } & A\left(\mathrm{~mm}^{2}\right) & \bar{x}(\mathrm{~mm}) & \bar{y}(\mathrm{~mm}) \\ \hline 1 & 400 \times 250=100000 & 200 & 125 \\ \hline 3 & \frac{1}{2} \times 150 \times 250=18750 & 400+\frac{150}{3}=450 & \frac{250}{3}=83.333 \\ 2 & \pi \times 60^{2}=11309.73355 & 200 & 125 \\ \hline \end{array} $$

\(X\) -component of the centroid.

\(\begin{aligned} \bar{X} &=\frac{A_{1} X_{1}-A_{2} X_{2}+A_{3} X_{3}}{A_{1}-A_{2}+A_{3}} \\ \bar{X} &=\frac{(100000 \times 200)+(18750 \times 450)-(11309.73355 \times 200)}{(100000+18750)-11309.73355} \\ &=\frac{26175553.29}{107440.2665} \\ &=243.63 \mathrm{~mm} \\ \bar{X} &=244 \mathrm{~mm} \end{aligned}\)

\(\bar{y}\) -component of the centroid. \(\bar{y}=\frac{A_{1} y_{1}-A_{2} y_{2}+A_{3} y_{3}}{A_{1}-A_{2}+A_{3}}\)

\(\begin{aligned} \bar{X} &=\frac{(100000 \times 125)+(18750 \times 83.333)-(11309.73355 \times 125)}{(100000+18750)-11309.73355} \\ &=\frac{12648777.06}{107440.2665} \\ &=117.728 \mathrm{~mm} \\ \bar{y} &=117.7 \mathrm{~mm} \end{aligned}\)

Answer 2

243.6,117.7