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<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 \(1000\pi\) cm\(^3\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">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.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find, in terms of \(a\), the value of \(r\) that minimises \(V\). (You need not show that your answer gives a minimum.)</span><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 \(1000\pi\) 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

2025 ACJC P1 Q6

2025 ACJC P1 Q6