Question

A board game has dice shaped like octahedrons. Each edge of the dice has length 2 cm, and h = %5Csqrt%7B2%5C%5C" id="TexFormula1" title="\sqrt{2\\" alt="\sqrt{2\\" align="absmiddle" class="latex-formula">/2 cm. What is the volume of each die? Round to the nearest hundredth.

Answer 1

Answer:

The answer is "734.68".

Step-by-step explanation:

Given value:

edge length = 2 cm

height = $\frac{\sqrt{2}}{2} \ cm$

volume = ?

$\sqrt{2} = 1.41\\\\ \sqrt{3}= 1.73$

$\ Area \ of \ hexagon \ = \frac{3 \sqrt{3}}{2} a^2\\\\\ Area = \frac{3 \sqrt{3}}{2} \times 2^2 \\\\\ Area = \frac{3 \sqrt{3}}{2} \times 2 \times 2 \\\\\ Area = 3 \sqrt{3} \times 2 \\\\\ Area = 6\sqrt{3} \\\\\ Area = 10.39$

$\ volume \ of \ octahedrons \ = \ Area \ of \ hexagon \times \ height$

                                        $= 10.39 \times \frac{\sqrt{2}}{2} \\\\= 734.68$