<p>A piece of vanguard sheet, \(ABCDEF\), is in the form of a regular hexagon of side \(a\) cm. A kite shape is cut out from each corner to form the shaded shape, as shown in Fig. \(1\). It is then folded to form the open hexagonal box of height \(h\) cm, as shown in Fig. \(2\).</p>
<p>Show that the volume \(V\) of the box in cm\(^3\) is given by \(V = 2\sqrt{3} h\left(\frac{\sqrt{3}}{2}a - h\right)^2.\)</p>
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A piece of vanguard sheet, \(ABCDEF\), is in the form of a regular hexagon of side \(a\) cm. A kite shape is cut out from each corner to form the shaded shape, as shown in Fig. \(1\). It is then folded to form the open hexagonal box of height \(h\) cm, as shown in Fig. \(2\).

Show that the volume \(V\) of the box in cm\(^3\) is given by \(V = 2\sqrt{3} h\left(\frac{\sqrt{3}}{2}a - h\right)^2.\)

Applications of Differentiation

International Baccalaureate Higher Level Mathematics

2015 AJC P1 Q11 (Modified) IP2U11 HOT Q1

2015 AJC P1 Q11 (Modified) IP2U11 HOT Q1

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