Question : A prism has a regular hexagonal base with a side of 6 cm. If the total surface area of the prism is 216$\sqrt3$ cm2, then what is the height (in cm) of the prism?
Option 1: $3\sqrt3$
Option 2: $6\sqrt3$
Option 3: $6$
Option 4: $3$
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Correct Answer: $3\sqrt3$
Solution : Given: Side, $a$ = 6 cm Let the height be $h$. Area of the base of the hexagonal prism $=6 \times \frac{\sqrt3}{4}a^2=6 \times \frac{\sqrt3}{4} \times 6^2 = 54\sqrt3$ Total curved surface area of prism = 2 × (Area of base) + 6 × (Side of the base) × height ⇒ $216\sqrt3 = 2 \times 54\sqrt3 + 6 \times 6 \times h$ ⇒ $108\sqrt3 = 36h$ $\therefore h = 3\sqrt3\ \text{cm}$ Hence, the correct answer is $3\sqrt3$.
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