The volumes of two similar figures are 343 mm3 and 512 mm3. If the surface area of the larger figure is 192 mm2, what is the surface area of the smaller figure?

In geometry, similar figures are those whose ratios of the corresponding sides are equal and the corresponding angles are congruent. In relation to the volume, we determine first the cube roots of the given and find the ratio as shown below.

s1 / s2 = cube root of (512/343)

= 8/7

The square of this ratio is the ratio of the areas of the figure. If we let x be the area of the smaller figure then,

(8/7) ^2 = 192 mm² / x

The value of x from the equation is 147 mm².

The area therefore of the smaller figure is 147 mm².