Question

A soild cube is cut into eight cubes of equal volumes.find the ratio of the total surface area of the given cube and that of one smaller cube

Answer 1

Let the side of original cube(larger cube) be  A units.
And let the side of new cube(small cube) be a units.

Now, volume of larger cube = 8 × volume of one small cube
          
           A³  =  8 × a³
         ⇒ A = 2a                 (By taking cube root both sides)
       
Now, Total surface area of cube =  6 × Side²

⇒ Ratio of total surface area of given cube to that of small cube will be :
 
      6 × A² : 6 × a²
     
     ⇒ 6 × (2a)² : 6 × a²                    (Putting A = 2a)
      ⇒ (2a)² : a²
     ⇒ 4a² : a²
     ⇒ 4 : 1

∴Ratio of total surface area of the given cube to that of one smaller cube = 4:1.