Question

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.

Answer 1

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`