A rectangular block is sprayed grey on all the four faces before it is cut into 24 identical cubes as shown in the diagram. The total surface area of the 24 individual cubes is 2200 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 24 identical cubes
= 24 x 6
= 144

Number of faces of the original block
= (12 + 12 + 4) x 2 
= 56

Difference in area of the faces
= 144 - 56 
= 88

Area of 88 faces = 2200 cm²
 
Area of 1 face
= 2200 ÷ 88
= 25 cm² 

Side of 1 cube
= √25
= 5 cm

Volume of 1 cube
= 5 x 5 x 5
= 125 cm³ 

Volume of the original block
= 24 x 125
= 3000 cm³

Answer(s): 3000 cm³