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Solution


Q.

The largest possible hemisphere is drilled out from a wooden cubical block of side 21 cm such that the base of the hemisphere is on one of the faces of the cube. Find the total surface area of the remaining solid.

Ans.

(2992.5)

Diameter of hemisphere = side of the cube = 21 cm

∴ radius of hemisphere = 21/2 cm

Total surface area of remaining solid = TSA of cube – base area of hemisphere + CSA of hemisphere = 6a2-πr2+2πr2=6a2+πr2

=6(21)2+227×(212)2=2646+227×212×212=2646+346.5=2992.5 cm2