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Question 46
A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?
Solution
Let the original length of each side of cube=3l
Surface area of the sphere=$$6*(3l)^{2}$$
=$$54(l)^{2}$$
Now length of each smaller cube=l
Total surface area of 27 cubes=$$27*6*(l)^{2}$$
=162$$(l)^{2}$$
percentage change in the surface area=((162$$(l)^{2}$$-$$54(l)^{2}$$)/$$54(l)^{2}$$)*100
=200%
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