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Surface Areas and Volumes
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27/06/2021 12:03 pm
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A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
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27/06/2021 12:05 pm
Diameter of hemisphere = Edge of the cube = l
Radius of hemisphere = l/2
∴ The total surface area of solid = surface area of cube + CSA of hemisphere – Area of base of hemisphere
TSA of remaining solid = 6 (edge)2 + 2πr2 - πr2
= 6l2 πr2
= 6l2 + π(l/2)2
= 6l2 + πl2/4
= l2/4(24 + π) sq. units