A group of student councillors bought an $8$ m long piece of tarpaulin canvas to build a tentage f

Question

A group of student councillors bought an $8$ m long piece of tarpaulin canvas to build a tentage for a school event. The canvas would extend diagonally at an angle of $\theta $ from the ground to a height of $3$ m, where it will then stretch horizontally to the school building (see diagram for the cross-sectional view). Given that the total cross-sectional area covered by the canvas is $A\mathrm{ }{{\mathrm{m}}^{2}}$, show that $A=24-9\operatorname{cosec}\theta +\frac{9}{2}\cot \theta $.[2] Find, by differentiation, the largest possible value of $A$.[5]

Accepted Answer

(i) $A=24-9 \text{cosec} \theta+\frac92\cot\theta$ (ii) $A_{\max}=24-\frac{9\sqrt3}{2}\text{ m}^2$

2015 HCI P1 Q4

2015 HCI P1 Q4

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