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A cube of side 5 cm is cut into as many

Question:

 A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface areas of the original cube to that of the sum

of the surface areas of the smaller cubes?

Solution:

Surface area of a cube = 6 a2, where a is side of a cube.
 ... Side of cube = 5cm 

... Surface area of the cube = 6 x (5)2 = 6 x 25

= 150cm2

Now, surface area of the cube with side 1 cm = 6 x (1)2= 6 cm2

 ... Surface area of 5 cubes with side 1 cm = 5 x 6 = 30 cm2

Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes

=30/150=3/15=1:5

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