?A solid cube of side 12cm is cut into 8 cubes of equal volume . What will be the side of the new cube ? Also , find the ratio between their surface areas.

Answers (1)

Solution :  Let the length of the side of new  cube be x cm . Then , 

               Volume of 8 cubes each of side x cm =    Volume of solid cube of side 12 cm . 

Rightarrow           8x^3=12^3

Rightarrow             x^3=6^3 Rightarrow x=6

Hence , the side of the new cube is 6 cm .

Now ,        S_1= surface area of solide cube of side 12 cm = 6 	imes 12^2 cm^2       

                  S_2= Surfae area of 8 cubes each of side 6 cm =8(6	imes 6^2)cm^2

	herefore              fracS_1S_2= frac6	imes 12^28	imes 6 	imes 6^2=frac12

Hence , required ratio = S_1: S_2=1:2.  

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