Q27 of 56 Page 13

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid (CBSE 2014)


According to the question,

Diameter of hemisphere = Edge of cube = l


Radius of hemisphere =

Curved Surface Area of hemisphere = 2 π r2

Surface Area of cube = (Edge)3

Total surface area of solid = Surface area of cubical part + CSA of hemispherical part - Area of base of hemispherical part


= 6 (Edge)2 + 2πr2 – πr2


= 6 (Edge)2 + πr2


TSA of Solid = 6l2 + π x ()2





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