The diagram below shows the design of a viewing platform. The viewing platform is designed by removi

Question

The diagram below shows the design of a viewing platform. The viewing platform is designed by removing two identical semi-circles at the ends of a rectangle. The radius of the semi-circle is $x$ m and the length of the rectangle is $y$ m. The enclosed area of the viewing platform is $10800$ m${}^2$. Show that $y = \frac{5400}{x} + \frac{\pi}{2}x$.[2] Tiles are to be laid along the perimeter, $P$ m, of the enclosed area of the viewing platform. Hence find an expression for $P$, in terms of $x$.[2] Find the exact value of $x$ which gives $P$ a minimum value. You need not justify that $P$ is a minimum value.[3] In another design, the area of the viewing platform, region $R$, is bounded by the line $y = -x + 4$, the curve $y = \sqrt{11 - 2x}$ and the $x$-axis. Given that both the line $y = -x + 4$ and the curve $y = \sqrt{11 - 2x}$ intersect at point $A$, verify that the coordinates of $A$ is $(1, 3)$.[1] Hence, without using a graphing calculator, find the area of region $R$.[4]

Accepted Answer

(a)(ii)$3\pi x+\frac{10800}{x}$ (a)(iii)$\frac{60}{\sqrt{\pi}}$ (b)(ii)4.5

2024 MI H1 Q6

2024 MI H1 Q6

Solution:

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