5. A hemispherical depression is cut out from one face of a cubical wooden block such
that the diameter 1 of the hemisphere is equal to the edge of the cube. Determine the
surface area of the remaining solid.
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Consider the diagram shown below.
It is given that a hemisphere of radius
2
l
is cut out from the top face of the cuboidal wooden block.
Therefore, surface area of the remaining solid
= surface area of the cuboidal box whose each edge is of length l − Area of the top of the hemispherical part + curved surface area of the hemispherical part
=6l
2
−πr
2
+2πr
2
=6l
2
−π(
2
l
)
2
+2π(
2
l
)
2
=6l
2
−
4
πl
2
+
2
πl
2
=
4
l
2
(24+π) sq.units
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