A rectangular block is sprayed grey on all the six faces before it is cut into 36 identical cubes as shown in the diagram. The total surface area of the 36 individual cubes is 17424 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 36 identical cubes
= 36 x 6
= 216

Number of faces of the orginal block
= (18 + 12 + 6) x 2 
= 72

Difference in area of the faces
= 216 - 72 
= 144

Area of 144 faces = 17424 cm²
 
Area of 1 face
= 17424 ÷ 144
= 121 cm² 

Side of 1 cube
= √121
= 11 cm

Volume of 1 cube
= 11 x 11 x 11
= 1331 cm³ 

Volume of the original block
= 36 x 1331
= 47916 cm³

Answer(s): 47916 cm³