Correct Answer - Option 3 : 300%
Given:
A solid cube is cut into 64 identical cubes.
Formula used:
Volume of a cube = (side)3
Calculation:
Let side of a bigger cube and smaller cube be A and a respectively.
A3 = 64 × a3
⇒ A = 4a
Total surface area of a bigger cube = 6A2 = 6 × (4a)2 = 96a2
Total surface area of 64 smaller cubes = 64 × 6a2 = 384a2
Percent increase in the total surface area = \(\frac{{384{a^2} - 96{a^2}}}{{96{a^2}}}\) × 100
⇒ \(\frac{{288{a^2}}}{{96{a^2}}}\) × 100 = 300%
∴ The percentage increase in the total surface area is 300%.
