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Question

A cubical block of side $$7\ cm$$ is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.


Solution


As per the question we can draw the diagram, 
The diagram shows that the greatest diameter possible for such hemisphere is equal to the length of cube edge, i.e., $$7$$cm.
Radius $$(r)$$ of hemispherical part  $$=\dfrac{7}{2}$$ $$= 3.5$$cm

Total surface area of solid $$=$$ Surface area of remaining cubical part $$+$$ CSA of hemispherical part $$+$$ Area of base of hemispherical part

                                            $$=6(Edge)^2 + 2\pi r^2- \pi r^2 \\= 6(Edge)^2+ \pi r^2$$

                                            $$=6(7)^2+\dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}$$

                                            $$=294 + 38.5 $$

                                           $$=332.5$$ $$cm^2$$

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Mathematics
RS Agarwal
Standard X

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