Answer:
200 cm²
Explanation:
The scale factor for areas of similar figures is the square of the scale factor relating their linear dimensions. For volumes of similar figures, the scale factor is the cube of the linear dimension scale factor. Together, these relations mean the area scale factor is the 2/3 power of the area scale factor.
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The larger surface area is ...
(50 cm²) × 8^(2/3) = (50 cm²) ×4 = 200 cm²
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Additional comment
The linear dimension scale factor is the cube root, or 1/3 power, of the volume scale factor. The area scale factor is the square of that or the 1/3 power times 2, the 2/3 power.
sf = ∛(v2/v1) = (v2/v1)^(1/3)
a2/a1 = sf^2 = ((v2/v1)^(1/3))^2 = (v2/v1)^(2/3)