Since the radiation effect is spread over a distance of 1 cm from the cube, we need to find all the points which are at a distance of 1 cm or less from the surface of the cube.

To simplify the understanding of the volume of the space influenced by the radiation effect, we divide the total volume in parts of known shape.

Consider the radiation effect spread over a distance of 1 cm from all the 6 faces of the cube.

In this case, we consider the volume of the space influenced by radiation effect caused by one face, and it will be of the shape of a cube of side 1 cm. Refer the diagram.

∴ Total volume of the space influenced by radiation effects caused by all the 6 faces = 6 × volume of the space influenced by one of the faces

= 6 × (1 × 1 × 1)

= 6 cm

^{3}Now, consider the additional radiation effect spread over a distance of 1 cm from all the 12 edges of the cube.

In this case, we consider the extra volume of the space influenced by radiation caused by one edge, and it will be of the shape of a quarter cylinder of radius 1 cm and height 1 cm. Refer the diagram.

∴ Total extra volume of the space influenced by radiation effect caused by all the edges = 12 × volume of the space influenced by one of the edges

Now, consider the additional radiation effect spread over a distance of 1 cm from all the 8 vertices of the cube.

In this case, we consider the extra volume of the space influenced by the radiation effect caused by one of the vertices, and it will be of the shape of 1/8

^{th} part of a sphere of radius 1 cm. Refer the diagram.

∴ Total extra volume of the space influenced by the radiation effect caused by all the vertices = 8 × volume of the space influenced by one of the vertices

∴ Total volume of the space influenced by radiations around the cube

Hence, option 3.