Question

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?

Answer 1

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