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Question

A cubical block of side 7 cm is surmounted by a hemisphere. Find the surface area of the solid(in cm2 ).


  1. 332.5 cm2

  2. 346.8 cm2 

  3. 312.5 cm2 

  4. 320 cm2 


Solution

The correct option is A

332.5 cm2


The hemisphere surmounts the cube, the maximum diameter the hemisphere can have = side of cube as shown in the figure below. The hemisphere will just touch the sides of top face of the cube.

Therefore, maximum diameter Hemisphere can have = 7 cm 

 Radius of Hemisphere =  r = 72=3.5 cm 



Surface area of solid  =  Surface area of 5 Faces of cube +  Surface area of Hemisphere + Surface area left uncovered on the top face of the cube (shown in blue)

=5l2+2.π.r2+ Area of Square ABCD  - Area of inscribed circle in square ABCD

=(5×7×7)+(2×227×3.5×3.5)+(49(227×3.5×3.5))

=245+77+(4938.5)=322+10.5=332.5 cm2 

The surface area of combined solid = 332.5 cm2

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