A cube of side 4 cm is cut into 1 cm. What is the ratio of the surface area of the original cubes and the cut-out cubes?
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Answer:
Surface area of cube of side 4 cm =6 ×4×4= 96 square cm.
Surface area of cube of side 1 cm = 6×1×1= 6 square cm .
Now when the 4 cm cube is divided into cutouts of 1 cm cubes,it will be divided into 64 cubes. This can be understood by imagining a 4 ×4 cube as follows
Surface area of 64 cubes of side 1 cm=64×6= 384 square cm.
Then the ratio of original to the cutouts will be = 96/384 =1/4 or 0.25
So the answer is 1/4.
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