Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
$ABCDE$ is the cross-section of a uniform prism whose centre of mass lies in the section, and it is in equilibrium with $DE$ resting on a horizontal surface. The cross-section is a square $OBCD$ of side length $a\,\text{m}$, from which a quadrant $OAE$ of a circle with radius $1\,\text{m}$ has been cut away (see diagram).
(i)[5]
Determine the distance from $O$ to the centre of mass of the prism, expressing your answer in terms of $a$, $\pi$, and $\sqrt{2}$.
(ii)[4]
Hence prove that $3a^2(2 - a) < \frac{3}{2}\pi - 2$, and check that this inequality is satisfied by $a = 1.68$ but not by $a = 1.67$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determines $OG_{\text{quadrant}} = \frac{2\sin(\pi/4)}{3\pi/4}$” …