A rectangular block is sprayed grey on all the four faces before it is cut into 20 identical cubes as shown in the diagram. The total surface area of the 20 individual cubes is 10368 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 20 identical cubes
= 20 x 6
= 120

Number of faces of the original block
= (10 + 10 + 4) x 2 
= 48

Difference in area of the faces
= 120 - 48 
= 72

Area of 72 faces = 10368 cm²
 
Area of 1 face
= 10368 ÷ 72
= 144 cm² 

Side of 1 cube
= √144
= 12 cm

Volume of 1 cube
= 12 x 12 x 12
= 1728 cm³ 

Volume of the original block
= 20 x 1728
= 34560 cm³

Answer(s): 34560 cm³