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Home » 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.
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.
CBSE | Class 10 | Exercise 13.1 | Maths | NCERT | Surface Areas And Volumes
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.

The graph is as per the following:

Ncert solutions class 10 chapter 13-6

Presently, the breadth of side of the equator = Edge of the 3D square = l

In this way, the span of half of the globe = l/2

∴ The all out surface space of strong = surface space of block + CSA of half of the globe – Area of base of side of the equator

TSA of staying strong

    \[=\text{ }6\text{ }\left( edge \right)^2+2\pi r^2-\pi r^2\]

    \[=\text{ }6l^2\text{ }\pi r^2\]

    \[=\text{ }6l^2+\pi \left( l/2 \right)^2\]

    \[=\text{ }6l^2+\pi l^2/4\]

    \[=\text{ }l^2/4\left( 24+\pi \right)\text{ }sq.\text{ }units\]

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