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Q.

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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a

Question Image

b

Question Image

c

Question Image

d

Question Image 

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 hemisphereQuestion Image Surface area of cube =Question Image
Curved surface area of hemisphere = Question Image
Area of base of hemisphere = Question ImageTotal surface area of remaining block = Surface area of the block area of base of hemisphere + Curved surface area of hemisphere
Question ImageVolume of cube =Question Image  Volume of hemisphere =Question Image Volume of remaining block = Volume of cube – volume of hemisphereQuestion Image Volume of the hemisphere block =Question ImageSo, option 3 is correct.
 
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