Как да изчислим Hexagonal Prism
Какво е Hexagonal Prism?
A hexagonal prism has two regular hexagonal bases connected by six rectangular faces. It appears in honeycomb structures, pencils, and crystals.
Формула
A_base = (3√3/2)a²; V = A_base × h; LSA = 6ah; TSA = 2A_base + 6ah
- a
- side length (regular hexagon) (length)
- h
- height of prism (length)
- V
- volume (length³)
Ръководство стъпка по стъпка
- 1Base area = (3√3/2) × a²
- 2Volume = Base area × height
- 3Lateral surface = 6 × a × h
- 4Total surface = 2 × Base + Lateral
Worked Examples
Вход
a = 4, h = 10
Резултат
Volume = (3√3/2)×16×10 = 415.69
Вход
a = 5, h = 8
Резултат
Volume ≈ 519.62
Frequently Asked Questions
Why is the hexagonal prism so common in nature?
Honeycombs use hexagonal prisms because they tile efficiently and require minimal material for maximum volume.
How many faces, edges, and vertices does a hexagonal prism have?
8 faces (2 hexagons + 6 rectangles), 18 edges, and 12 vertices.
Is a hexagonal prism the same as a hexagonal cylinder?
No, a prism has flat rectangular sides, while a cylinder would have curved sides.
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