Question

A board game has dice shaped like octahedrons. Each edge of the dice has length 2 cm, and h =
`\sqrt{2\\`/2 cm. What is the volume of each die? Round to the nearest hundredth.

Answer 1

The answer is "734.68".

Explanation:

Given value:

edge length = 2 cm

height =
`(√(2))/(2) \ cm`

volume = ?

`√(2) = 1.41\\\\ √(3)= 1.73\\`

`\ Area \ of \ hexagon \ = (3 √(3))/(2) a^2\\\\\ Area = (3 √(3))/(2) * 2^2 \\\\\ Area = (3 √(3))/(2) * 2 * 2 \\\\\ Area = 3 √(3) * 2 \\\\\ Area = 6√(3) \\\\\ Area = 10.39 \\`

`\ volume \ of \ octahedrons \ = \ Area \ of \ hexagon * \ height \\\\`

`= 10.39 * (√(2))/(2) \\\\= 734.68\\`