A rectangular block is sprayed grey on all the four faces before it is cut into 30 identical cubes as shown in the diagram. The total surface area of the 30 individual cubes is 472 cm² more than the surface area of the original block that is sprayed grey. What is the volume of the rectangular block?
Number of faces of the 30 identical cubes
= 30 x 6
= 180

Number of faces of the orginal block
= (15 + 10 + 6) x 2 
= 62

Difference in area of the faces
= 180 - 62 
= 118

Area of 118 faces = 472 cm²
 
Area of 1 face
= 472 ÷ 118
= 4 cm² 

Side of 1 cube
= √4
= 2 cm

Volume of 1 cube
= 2 x 2 x 2
= 8 cm³ 

Volume of the original block
= 30 x 8
= 240 cm³

Answer(s): 240 cm³