QUESTION $1$

$1\mathrm{.}1$ Determine the co$-$ordinates of the centroid of the first quadrant area bounded by the

parabola $y=9-x^2$ as shown in Figure Q$1\mathrm{.}1.$

$1\mathrm{.}2$ A steel beam is of I$-$section is shown in Figure Q$1\mathrm{.}2.$ Determine:

$1\mathrm{.}2\mathrm{.}1$ The moment of inertia about its centroid C$.$ G$.$ along the horizontal axis $x-x$ and the

vertical axis $Y-Y$; and

$1\mathrm{.}2\mathrm{.}2$ The moment of inertia about the new axes which is turned through an angle of $60$

anticlockwise to the old axes.