Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
The diagram represents a uniform lamina $ABCDEFGH$. It is built from a quarter-circle $OAB$ with radius $r\,\text{m}$, a rectangle $DEFG$, and two isosceles right-angled triangles $COD$ and $GOH$. In the rectangle, $DG = EF = r\,\text{m}$ and $DE = FG = x\,\text{m}$.
(i)[6]
If the centre of mass of the lamina is at $O$, express $x$ in terms of $r$.
(ii)[1]
If the rectangle $DEFG$ is now a square with side length $r\,\text{m}$, state, with a reason, whether the centre of mass of the lamina is inside the square or inside the quarter-circle.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that the centre of mass of each triangle is $r/6$ below $O$” …