Question

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

Answer 1

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.