Question
A crystal is in the form of a regular octahedron. The edges of the octahedron are all 4mm long. Calculate the volume of the octahedron?
Answers
GPT 3.5
To find the volume of an octahedron, we can use the formula:
Volume = (1/3) * √2 * a^3
where a is the length of the edge of the octahedron.
Given that a = 4mm, we can substitute this into the formula:
Volume = (1/3) * √2 * 4^3
Volume = (1/3) * √2 * 64
Volume = (1/3) * 8√2
Volume = 8√2 / 3
Approximately, the volume of the octahedron is 9.42 cubic mm.
Volume = (1/3) * √2 * a^3
where a is the length of the edge of the octahedron.
Given that a = 4mm, we can substitute this into the formula:
Volume = (1/3) * √2 * 4^3
Volume = (1/3) * √2 * 64
Volume = (1/3) * 8√2
Volume = 8√2 / 3
Approximately, the volume of the octahedron is 9.42 cubic mm.