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# A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also, find the surface area of the solid.

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ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10
A cubical block side is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also, find the surface area of the solid.
This is the Question Number 07, Exercise 17.4 of M.L Aggarwal.

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1. Given edge of the cube, a = 7 cm

Diameter of the hemisphere, d = 7 cm

Radius, r = d/2 = 7/2 = 3.5 cm

Surface area of the hemisphere = 2r2

= 2Ã—(22/7)Ã—3.52

= 44Ã—12.25/7

= 539/7

= 77 cm2

Surface area of the cube = 6a2

= 6Ã—72

= 6Ã—49

= 294 cm2

Surface area of base of hemisphere = r2

= (22/7)Ã—3.52

= 22Ã—12.25/7

= 38.5 cm2

Surface area of the solid = surface area of the cube + surface area of hemisphere â€“ surface area of the base of hemisphere

= 294+77-38.5

= 332.5 cm2

Hence the surface area of the solid is 332.5 cm2.

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