A cube with edges of length b is divided into 8 equal smaller cubes. Calculate the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube.
A
32b2
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B
34b2
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C
92b2
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D
6b2
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E
12b2
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Solution
The correct option is C6b2 Surface area of original cube is 6b2 Volume of cube is b3 Volume of smaller cube is b38, which implies side length of smaller cube is b2 Surface area of 8 smaller cubes combined is 8×6×b22=12b2 Difference is 12b2−6b2=6b2