  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  $$=\dfrac{7}{2}$$ $$= 3.5$$cmTotal surface area of solid $$=$$ Surface area of remaining cubical part $$+$$ CSA of hemispherical part $$+$$ Area of base of hemispherical part                                            $$=6(Edge)^2 + 2\pi r^2- \pi r^2 \\= 6(Edge)^2+ \pi r^2$$                                            $$=6(7)^2+\dfrac{22}{7}\times \dfrac{7}{2}\times \dfrac{7}{2}$$                                            $$=294 + 38.5$$                                           $$=332.5$$ $$cm^2$$ MathematicsRS AgarwalStandard X

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