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

Edge of wooden block (a) = 21 cm


Diameter of hemisphere = edge of cube


Radius = 21/2 = 10.5 cm


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




= 6835.5 cm3


Surface area of box = 6a2 ………… (1)


Curved surface area of hemisphere = 2πr3 ……….. (2)


Area of base of hemisphere ……………….. (3)


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




= 2992.5 cm2


Remaining surface area of box=2992.5 cm2


Volume of remaining block=6835.5 cm3


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