A piece of vanguard sheet, $ABCDEF$, is in the form of a regular hexagon of side $a$ cm. A kite

Question

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 $V = 2\sqrt{3} h\left(\frac{\sqrt{3}}{2}a - h\right)^2.$

Accepted Answer

$V=2\sqrt3h\left(\frac{\sqrt3}{2}a-h\right)^2\text{ cm}^3$

2015 AJC P1 Q11 (Modified) IP2U11 HOT Q1

2015 AJC P1 Q11 (Modified) IP2U11 HOT Q1

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