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

Given:

Side of Cube = l

Diameter of Hemisphere = l

So, the Radius of Hemisphere = $\frac{l}{2}$

To Find:

Surface Area of Remaining Solid.

Solution:

For finding the Surface area of remaining solid,

Firstly, one of the surface sides should be subtracted from the cube.

                                   $S.A. Solid = S.A.Cube - l^{2}$

Then, the Curved Surface Area of the hemisphere should be added as it has been carved out from the cube, which will increase its surface area.

So,

                               $S.A.Solid = S.A.Cube - l^{2} + 2\pi l^{2}$