The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?(1 point) Responses 16 mm2mm216 mm squared 68 mm2mm268 mm squared 216 mm2mm2216 mm squared 147 mm2
Since the two solids are similar, their volumes are proportional to the cube of their scale factor (since volume is a three-dimensional measurement).
Let the scale factor be x. So, we have:
(857.5 / 540) = x^3
1.588 = x^3
x ≈ 1.1144
The surface area of similar solids is proportional to the square of their scale factor (since surface area is a two-dimensional measurement).
So, the surface area of the larger solid is:
(108)(1.1144)^2 = 136.08 mm^2
Therefore, the surface area of the larger solid is 136.08 mm^2.