A cube whose edge measures 8 cm is cut into cubes whose edge measures 1 cm. Find the ratio of the surface area of the original cube to the sum of the surface areas of the new cube ?
Let a1=edge of whole cube=8cm Then V1=(a1*a1*a1)=(8*8*8)512cm^3 a2=edge of cut cube=1cm Then V2=(a2*a2*a2)=(1*1*1)=1cm^3 No of cubes=N=V1 /V2=512/1=512nos A1=Surface area of whole cube =(6*a1*a1)=(6*8*8)=384cm^2 A2=Total surface area of cut cubes =N*(6*a2*a2)=512*(6*1*1)=3072 A1/A2=384/3072 =1:8 Ans is 1:8
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