A prism has a regular hexagonal base with side 8 cm and the total surf

1.	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 cm2. 15√6 cm3. 13√3 cm 4. 15√3 cm
Answer» Correct Answer - Option 4 : 15√3 cm 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

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 cm2. 15√6 cm3. 13√3 cm 4. 15√3 cm

Answer» Correct Answer - Option 4 : 15√3 cm

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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