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Bunuel
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Bigger cube has each side measuring 3, SA is 54. Smaller will have each side measuring half of the bigger cube, 1.5. SA of smaller cube is 13.5. So the answer is B, 40.5

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A cube with volume 27 is cut into 8 smaller cubes having equal volumes. What is the difference between the surface area of the original cube and the surface area of one of the smaller cubes?

(A) 45.25
(B) 40.5
(C) 27
(D) 24.38
(E) 19


Answer is B IMO

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Whenever a cube is divided into 8 parts, the ratio of side original: small is 2:1.

Now, as side of original cube is 3, side of small cube must be 1.5.

Difference in SA= (6*3^2)-(6*1.5^2)= 6(9-2.25)= 6*6.75= 6*(6+0.75)= 36+(6*3/4)= 36+4.5= 40.5

Ans B

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1. Using the idea of scale factor, a cube divided into 8 parts has a factor of k^3=8 or k=2.
2. So each side of large cube is twice as big as a small cube (side small = 3/2)
3. Find SA small cube, 6(3/2)^2 = 13.5
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