An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra and these have faces ranging form triangles to heptagons. The only single formula for the area is the sum of the areas of each of the faces.
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rectangle and octahedron
An octahedron is a term used to describe a 3-dimensional shape with 8 faces. The shape could be a heptagon based pyramid, a hexagon based prism, a quadrilateral dipyramid or some other shape. There will be different formulae for their surface areas and the only certain way is to measure the area of each face and add the areas together.
The formula for the surface area of a sphere is: 4 pi r 2
It depends on the formula that describes the surface itself. "Curved surface area" is not enough information to answer the question.
Given the surface area, where S=surface area, the formula for finding the volume isV = √(S / 4pi)