27 small cubic blocks of side 1 m are joined to form a bigger cube. Now, if one block is removed from each corner of the bigger cube, what will be the surface area (in m2) of the resultant object?
A
54
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B
46
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C
30
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D
27
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Solution
The correct option is A 54 Volume of one small cube = side3 = 13 = 1m3
Volume of the large cube = 27× volume of small cube = 27×1 = 27m3
Side of the large cube = 3√volume = 3√27 = 3 m
When a corner cube is removed, the surface area gets rerduced by area of 3 square faces. But, the surface area gets increased by the area of the 3 new square faces formed in the gap created by removal of the cube. ∴ Change in surface area = Increase by area of 3 square faces + Decrease by area of 3 square faces
= No change
∴ New surface area = Initial surface area
= 6side2
= 6×32
= 54m2