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.

Explanation

Please refer to video for grahical representation.

Here, required area can be given as,

`A = 5**`Surface Area of each face `+` Surface area of hemisphere`+` Area of top side

Also, Area of top side = Area of sixth face - Area of circular part

So,`A = 5l^2 +2pi(l/2)^2+(l^2-pi(l/2)^2)`

`A = 6l^2+pi(l^2/4)=l^2(6+pi/4) = 6.785l^2`