ardz24 wrote: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
Volume of a cube = e³.
Surface area of a cube = 6e².
Original cube:
Since V = 27, we get:
e³ = 27
e = 3.
Surface area = 6e² = 6(3²) = 54.
Smaller cubes:
Since the original cube with a volume of 27 is divided into 8 smaller cubes, the volume of each smaller cube = 27/8.
Thus:
e³ = 27/8
e = 3/2.
Surface area = 6(e²) = 6(3/2)² = 54/4 = 27/2 = 13.5.
Thus:
Difference between the surface areas = 54 - 13.5 = 40.5.
The correct answer is
B.
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