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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. [Use `pi = 22/7`]
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Solution
From the figure, it can be observed that the greatest diameter possible for such hemisphere is equal to the cube’s edge, i.e., 7cm.
Radius (r) of hemispherical part = `7/2` = 3.5 cm
Total surface area of solid = Surface area of cubical part + CSA of hemispherical part − Area of base of hemispherical part
= 6 (Edge)2 + 2πr2 - πr2
= 6 (Edge)2 + πr2
Total surface area of solid = `6(7)^2 + 22/7 xx 7/2xx 7/2`
= 294 + 38.5
= 332.5 cm2
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