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Question

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

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Solution


Given:
Diameter of hemisphere = Edge of the cube =l
Radius of hemisphere r=l2
Total surface area of solid = Surface area of cubical part + Closed Surface of hemisphere part - Area of base of hemispherical part

=6(Edge)2+2πr2πr2=6(Edge)2+πr2

Total surface are of solid = 6l2+π×(l2)2
= 6l2+πl24

=14[24+π]l2 sq. units

494880_465133_ans.PNG

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