Question

A jeweler is setting a stone cut in the shape of a regular octahedron. A regular octahedron is a solid with eight equilateral triangles as faces. The formula for the volume of the stone is V=0.47s³ , where s is the side length (in millimeters) of an edge of the stone. The volume of the stone is 161 cubic millimeters. Find the length of an edge of the stone.

Answer 1

Using the volume formula for a regular octahedron, V=0.47s³, and given the volume of 161 cubic millimeters, the side length of the octahedron is found to be approximately 7 millimeters.

Step-by-step explanation:

To find the side length of a stone that is cut in the shape of a regular octahedron, we have the volume formula V = 0.47s³, where V is the volume and s is the side length of the octahedron. Given that the volume of the stone is 161 cubic millimeters, we can solve for the side length s by plugging in the volume into the formula and solving for s.

The calculation would proceed as follows:

• 161 = 0.47s³
• s³ = 161 / 0.47
• s³ ≈ 342.55319149
• s ≈ ∛342.55319149
• s ≈ 7mm

Therefore, the side length of the stone is approximately 7 millimeters.