a cube is built using 64 smaller cubes of side 1cm.After it is built one cube is removed from each of the corners.Now calculate the total surface area of the formed solid
Answers
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
A cube of side 4 cm is cut in 1 cm cubes. What is the ratio of the surface of the original cube and cut outs?
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
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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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