Question

The base of a right prism is a regular hexagon that has side of 4 cm then, find the volume of the prism if its height is 12√3 cm.
1. 480 cm3
2. 600 cm3
3. 864 cm3
4. 840 cm3

Answer 1

Correct Answer - Option 3 : 864 cm3

Given:

The base of a right prism is a regular hexagon of side 4 cm

Its height is 12√3 cm

Formula used:

The volume of the prism = Area of base × Height

Area of regular hexagon = 6 × (√3/4)a²

Calculations:

According to the question, we have

The area of a regular Hexagon is 

Area of regular Hexagon = 6 × (√3/4)a²

⇒ Area = 6 × (√3/4) × (4)²

⇒ Area = 6 × √3 × 4

⇒ Area = 24√3 cm²

Hence, The volume of the prism is 

The volume of the prism = Area of base × Height

⇒ Volume = 24√3 × 12√3

⇒ Volume = 24 × 12 × 3

⇒ Volume = 864 cm³

∴ The Volume of the prism is 864 cm3.