Explanation:

Pyramid has a square base of side 4 cm. 
Height of the prism is 9 cm.
= > Slant height of the pyramid^2 = ( 9 cm )^2 + ( 4 / 2 cm )^2
= > Slant height of the pyramid^2 = 81 cm^2 + 4 cm^2 
= > Slant height of the pyramid^2 = 85 cm^2
When pyramid is cut in three parts of equal height, height of each part becomes ( 9 / 3 ) cm i.e. 3 cm.Also, length of slope of each part becomes √85 / 3 cm i.e. √( 85 / 9 ) cm.
Thus, 
= > Half of length of base of 1st part i.e. pyramid of height 3 cm = √[ √{ 85 / 9 } cm )^2 - ( 3 cm )^2 } 
= > Length of base of 1st part = 2 x √{ 85 / 9 cm^2 - 9 cm^2 } 
= > Length of base of 1st part = 2 x √{ ( 85 - 81 ) / 9 }
= > Length of base of 1st part = 2 x √{ 4 / 9 } 
= > Length of base of 1st part = 2 x 2 / 3
Slant height of pyramid is √85. 
So, slant height of pyramid in 1st part is 2 / 3 of √85 that is √( 340 / 9 ).
So, length of base of 2nd pyramid of height 6 cm is 2 x 4 / 3 cm. 
Thus,
= > Required ratio 
= > 1 / 3 x ( length x breadth x height ) of 1st part : 1 / 3 x ( length x breadth x height ) of 2nd part : 1 / 3 x ( length x breadth x height ) of 3rd part
= > ( length x breadth x height ) of 1st part : { ( length x breadth x height ) of 2nd and 1st part - ( length x height x breadth ) of 1st part } : { ( length x breadth x height ) of 3rd part, 2nd part and 1st part ) - ( length x height x breadth ) of 2nd and 1st part }
= > { ( 2 x 2 / 3 ) x ( 2 x 2 / 3 ) x 3 } : [ ( 2 x 4 / 3 x 2 x 4 / 3 x 6 ) - ( 2 x 2 / 3 x 2 x 2 / 3 x 3 ) ] : [ 4 x 4 x 9 - ( 2 x 4 / 3 x 2 x 4 / 3 x 6 ) ] 
= > 16 / 3 : ( 128 / 3 - 16 / 3 ) : ( 144 - 128 / 3 ) 
= > 64 : 112 : 304
= > 1 : 7 : 19
Hence the required ratio is 1 : 7 : 19.