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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.

5. 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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It is given that the diameter of the hemisphere is equal to the edge length of the cube. 

The total surface area of solid is given by :

The surface area of solid   =   Surface area of cube   +   Surface area of the hemisphere  -  Area of the base of the hemisphere

The surface area of the cube   =\ 6l^2

And surface area of the hemisphere:

 =\ 2\pi r^2\ =\ 2\pi \left ( \frac{l}{2} \right )^2

Area of base of the hemisphere:

 =\ \pi r^2\ =\ \pi \left ( \frac{l}{2} \right )^2

Thus the area of solid is:

=\ 6l^2\ +\ \pi \left ( \frac{l}{2} \right )^2\ unit^2

Posted by

Devendra Khairwa

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