Question

A hemispherical depression is cut out from one face
of a cubical wooden block such that the diameter 4
units of the hemisphere is equal to the edge of the
cube. Determine the surface area of the remaining
solid.​

Answer 1

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Surface Areas and Volumes

Surface Area of Spheres

A hemispherical depression ...

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Asked on November 22, 2019 byPoojita Kottu

A hemispherical depression is cut out from one face of the 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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ANSWER

Consider the diagram shown below.

It is given that a hemisphere of radius 2l 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

=6l2−πr2+2πr2

=6l2−π(2l)2+2π(2l)2

=6l2−4πl2+2πl2

=4l2(24+π) sq.units