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A hemispherical depression is cut from one face of a cubical wooden block of edge 21cm such that the diameter of hemisphere is equal to the edge of cube determine the volume and total surface area of the remaining block?

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Given edge of wooden block (a) = 21cm

Given diameter of hemisphere = edge of cube

Radius = 21/2 = 10.5cm

Volume of remaining block = volume of box – volume of hemisphere

Surface area of box = 6a2   ........(1)

Curved surface area of hemisphere = 2πr2   ..........(2)

Area of base of hemisphere = πr2

So remaining surface area of box = (1) – (2) + (3)

Remaining surface area of box = 2992.5cm2

Volume of remaining block = 6835.5cm3

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