Question
Download Solution PDFA prism has a regular hexagonal base with side 8 cm and the total surface area of the prism is 912√3 cm2, then what is the height of the prism?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The side of the prism = 8cm
The total surface area of the prism = 912√3 cm2
Formula used:
Area of the regular hexagon = 3√3/2 × side2
The total surface area of the prism = 2 × Area of the base + 6 × (Side of the base) × (Height of prism)
Calculation:
Let the height of the prism be h cm
Area of the regular hexagon = 3√3/2 × side2
⇒ 3√3/2 × 82
⇒ 96√3 cm2
The total surface area of the prism = 2 × Area of the base + 6 × (Side of the base) × (Height of prism)
⇒ 2 × 96√3 + 6 × 8 × h = 912√3
⇒ 6 × 8 × h = 720√3
⇒ h = 15√3
∴ The height of the prism is 15√3 cm
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