Mathematics
A cuboidal 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.
Mensuration
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Answer
Cuboidal block of side 7 cm is surmounted by a hemisphere as shown in figure below:
Side of cuboidal block = 7 cm.
Greatest diameter of hemisphere = 7 cm.
Radius =
= = 3.5 cm.
Surface area of the hemisphere = .
Putting values we get,
Surface area of the hemisphere =
Surface area of the cube = 6a2 = 6 x 72 = 6 × 49 = 294 cm2.
Surface area of base of hemisphere = πr2.
Putting values we get,
Surface area of base of hemisphere =
Surface area of solid = Surface area of cube + Surface area of hemisphere - Surface area of base of hemisphere = 294 + 77 - 38.5 = 332.5 cm2.
Hence, the greatest diameter that the hemisphere can have is 7 cm and surface area of the solid is 332.5 cm2.
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