<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1783531498997-mmzaoyvm5om.png" style="max-width: min(350px, 100%); height: auto; display: block;" alt="Figure 1 and Figure 2 showing the open cylindrical tank and its cross-sectional view." class="aligncenter custom-width" /></figure></div>
<p>Figure 1 shows an open cylindrical tank. Figure 2 shows the cross-sectional view of the tank. The external radius of the tank is \(r\) cm, the external height is \(h\) cm and the tank is made with a material of thickness \(a\) cm throughout. The internal volume of the tank is fixed at \(1000\pi\) \(\mathrm{cm}^3\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Show that the volume of the material needed to make the cylindrical tank is given by \(V = k\pi \left[ \frac{r^2}{(r-a)^2} - 1 \right] + \pi r^2 a\), where&nbsp;\(k\) is a constant to be determined.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find, in terms of \(a\), the value of \(r\) that minimises \(V\). (You need not show that your answer gives a minimum.)<span class="inline-marks">[3]</span></div></li></ol>

Figure 1 shows an open cylindrical tank. Figure 2 shows the cross-sectional view of the tank. The external radius of the tank is \(r\) cm, the external height is \(h\) cm and the tank is made with a material of thickness \(a\) cm throughout. The internal volume of the tank is fixed at \(1000\pi\) \(\mathrm{cm}^3\).

Show that the volume of the material needed to make the cylindrical tank is given by \(V = k\pi \left[ \frac{r^2}{(r-a)^2} - 1 \right] + \pi r^2 a\), where  \(k\) is a constant to be determined.

Find, in terms of \(a\), the value of \(r\) that minimises \(V\). (You need not show that your answer gives a minimum.)

Applications of Differentiation

International Baccalaureate Higher Level Mathematics

22025 ACJC P1 Q6

22025 ACJC P1 Q6