A solid is made by scooping out a hemispherical cavity from one face of a cube. Compared with the original cube, the total surface area of the new solid:

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decreases by the base circle area and increases by the hemisphere's curved area. Carving out removes the flat circle (π*r^2) from the cube face and adds the inner curved hemispherical surface (2*π*r^2).

A solid is made by scooping out a hemispherical cavity from one face of a cube. Compared with the original cube, the total surface area of the new solid:

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