A hemispherical depression is cut out from one face of a cubical wooden block, Determine the surface area of the remaining solid.

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

Solution:
Surface area of the cubical wooden box = 6(edge)²
Let the edge of a cube = l
∴ Surface area of a cube = 6(l)²
Diameter of a hemisphere = l
Radius of a hemisphere = l/2

=> Surface area of a hemisphere = 2p r²

Surface area of the remaining solid = Surface area of a cube - Surface area of a hemisphere