<p>A closed triangular prism has length \(l\) cm and an equilateral triangle of side \(x\) cm as its base.</p>
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<ol class="i-list"><li><div class="list-item-paragraph">Given that the total surface area of this prism is 150 cm\({}^2\), show that the volume \(V\) cm\({}^3\) of the prism is given by</div><div class="list-item-paragraph" style="text-align: center">\[V = \frac{1}{8}x\left(100\sqrt{3} - x^2\right).\]<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence using differentiation, find the value of the maximum volume of the prism, proving that it is a maximum.<span class="inline-marks">[4]</span></div></li></ol>

A closed triangular prism has length \(l\) cm and an equilateral triangle of side \(x\) cm as its base.

Given that the total surface area of this prism is 150 cm\({}^2\), show that the volume \(V\) cm\({}^3\) of the prism is given by

\[V = \frac{1}{8}x\left(100\sqrt{3} - x^2\right).\]

Hence using differentiation, find the value of the maximum volume of the prism, proving that it is a maximum.

2024 MI PRU2 P1 Q6

2024 MI PRU2 P1 Q6