64 identical cubes are cut from a big cube and all the smaller cubes are arranged in a row to form a long cuboid. What is the percentage increase in the total surface area of the cuboid over the total surface area of the cube?
Answer & explanation
Correct answer: option 2
The volume 64 smaller cubes = The volume of 1 bigger cube
64(edge1)³ = (edge2)³
4(edge1) = (edge2)
Let the edge of smaller cubes = 1 unit,
The edge of bigger cube = 4 units
The dimensions of the cuboid such formed = 64 x 1 x 1
Surface area of cuboid = 2(lb + bh + lh) = 2(64 + 1 + 64) = 258
Surface area of 1 bigger cube = 6 (4)² = 96
Surface area increased = 258 - 96 = 162
Percentage increase = \(\frac{162}{96}\) x 100 = 168.75%