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A hemispherical depression is cut out from one face of a cubical wooden block of edge 21 cm, such that the diameter of the hemisphere is equal to the edge of the cube. Determine the volume and total surface area of the remaining block.

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answer is C.

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Detailed Solution

Length of edge of the cube (a) = 21 cm
Diameter of hemisphere (d) = 21 cm
Hence,
Radius of the hemisphere

Surface area of cube =

Curved surface area of hemisphere =

Area of base of hemisphere =

Total surface area of remaining block = Surface area of the block area of base of hemisphere + Curved surface area of hemisphere
Question Image

Volume of cube =

Volume of hemisphere =

Volume of remaining block = Volume of cube – volume of hemisphere Question Image

Volume of the hemisphere block =

So, option 3 is correct.

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