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A right prism with base regular hexagon of side ‘x’ cm and height 5√3 cm have lateral surface area of the prism as 240√3 cm2, then what will be the volume of the prism?

A right prism with base regular hexagon of side ‘x’ cm and height 5√3 cm have lateral surface area of the prism as 240√3 cm2, then what will be the volume of the prism? Correct Answer 1440 cm<sup>3</sup>

GIVEN:

Lateral surface area of the prism is 240√3 cm2

Height of prism = 5√3 cm

CONCEPT:

Value of ‘x’ can be found with help of LSA.

FORMULA USED:

Lateral surface area of the prism = Perimeter of the base × Height

Volume of the prism = Base area × Height

Area of hexagon = 6 × (√3/4) × (side)2

CALCULATION:

Perimeter of the base of prism = 6 × x = 6x

Lateral surface area of the prism = 6x × 5√3 = 240√3

⇒ 6x = 48

⇒ x = 8 cm

Base area of the prism = 6 × (√3/4) × 82 = 96√3 cm2

⇒ Volume of the prism

⇒ 96√3 × 5√3

⇒ 1440 cm3

∴ volume of prism is 1440 cm3

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