Question

What will be the volume of a 10 m high prism whose base is a regular polygon with each side 2 m and internal angle of 120°? Given(√3 = 1.7)
1. 102 cm³
2. 204 m³
3. 51 m³
4. 102 m³

Answer 1

Correct Answer - Option 4 : 102 m³

Given-   

Height of prism = 10 m

Each Side of polygon = 2 m

Each interior angle = 120° 

Concept Used- 

Volume of Prism = Area of Base × Height 

Area of Hexagon = 3√3/2 × Side²

Each External Angle of a polygon = 360/n   [where n = number of sides of the polygon]

Calculation-

Exterior Angle = 180° - 120° 

⇒ 60° 

n = 360/60

⇒ 6

Hence the polygon is a regular hexagon.

Area of Hexagon = 3√3/2 × 2²

⇒ 6√3 m²

∴ Volume of Prism = 6√3 × 10     ∵ √3 = 1.7(given)

⇒ 102 m³