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A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm2, then what is the height (in cm) of prism?
- A3√3
- B6√3
- C6
- D3
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CCommunity
Area of the base of prism = 6 × √3/4 × 6 × 6 = 54√3
Total surface area of the prism = 2 × Area of the base + 6 × (Side of the base) × (Height of prism)
⇒ 216√3 = 2 × 54√3 + 6 × 6 × H
⇒ 36H = 108√3
∴ H = 3√3 cm
Total surface area of the prism = 2 × Area of the base + 6 × (Side of the base) × (Height of prism)
⇒ 216√3 = 2 × 54√3 + 6 × 6 × H
⇒ 36H = 108√3
∴ H = 3√3 cm