A 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?

  1. 13√6 cm
  2. 15√6 cm
  3. 13√3 cm 
  4. 15√3 cm

Answer (Detailed Solution Below)

Option 4 : 15√3 cm
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Detailed Solution

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Given:

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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