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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