MathematicsA cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?


  1. A
    1: 2
  2. B
    1: 3
  3. C
    1: 4
  4. D
    1: 6 

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    Solution:

    Given that,
    A cube of side 4 cm is cut into 1 cm cubes.
    We know,
    Volume of cube is given by a³.
    Surface area of cube is given by 6a², where a is the edge length of cube.
    Therefore, the surface area will be,
    ⇒Surface area=6× 4 2 ⇒Surface area=96c m 2  
    Now, volume of original cube with volume of l new cut out cube. Number of cubes =  4 3 1 3 ⇒Number of cubes = 64  
    The surface area will be,
    ⇒A= 6 × 1 2 ⇒A= 6 c m 2  
    Multiply with number of cubes (64) to find total surface area of cut out cubes, ⇒Surface area=64 × 6 ⇒Surface area=384c m 2  
    Now, the ratio of surface area of original cube to cut out cubes is,
    96:384 ⇒1:4  
    Hence, the required ratio is 1:4.
    Therefore, option 3 is correct.
     

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