Question

a solid cube of side 12 cm is cut into eight cubes of equal volume.what will be the side of the new cube?also find the ratio between their surface areas

Answer 1

the volume of cube will be 6cm cube

Answer 2

The side of original cube is 12cm

thus its volume=side³

                        = 12³
                        =1728 cubic cm

therefore,
             the volume of original cube is 1728 cubic cm.

It is given that it is divided equally in volume into 8 new cubes

           the volume of the new cube=$\frac{1728}{8}$
                                                       =216 cubic cm
therefore,
              the volume of new cube is 216 cubic cm

    volume of new cube= side³
                             216 = side

By taking cube root on both sides,
        
                              6   = side

thus,
the side of new cube is 6 cm

NOW, WE HAVE TO FIND THE RATIO OF SURFACE AREA OF ORIGINAL CUBE TO NEW CUBE

    Surface area of original cube=6 × side²
                                                  =6 × 12²
                                                  =6 × 144
                                                  =864 cm²
     
     Surface area of new cube    = 6 × side²
                                                  = 6 × 6²
                                                  = 6 × 36
                                                  = 216 cm²

     Ratio of Surface area  of original cube to surface area of new cube,
  
     Ratio=$\frac{Surface area of original cube}{Surface area of new cube }$
     
     Ratio=$\frac{864}{216}$
      
      Ratio=$\frac{216 * 4 }{216 * 1}$
     
       Ratio= 4 : 1

ANS. The side of new cube is 6 cm and THE RATIO of their surface areas is 4 : 1