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A cubic block of wood with side lengths of 10 cm is cut into smaller cubes with side lengths of $2$ cm. What is the ratio of the surface area of the larger block of wood to the combined surface area of the smaller blocks of wood? Express your answer as a common fraction.

 Sep 22, 2021
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Volume of larger cube  10 * 10 * 10 = 1000 cm^3

Volume of a smaller cube   2 * 2 * 2 = 8 cm^2               1000/8 = 125 smaller cubes

 

 

Surface area of large cube = 10*10 * 6 = 600 cm^2

                        smaller cube = 2 * 2 * 6 = 24 cm^2    

                                                                 and there is 125 of them , so total surface area = 125 * 24 = 3000 cm^2

 

600 / 3000 = 1/5

 Sep 22, 2021

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