Can't figure this out

Question

I know how to do the reverse version of this question but I don't know how to do this part: The surface areas of two similar solids are 356 yd^2 and 1058 yd^2. The volume of the larger solid is 1754 yd^3. What is the volume of the smaller solid?

Answer 1

Before delving into just the calculation part, something that helps me is to consider the following:

lengths are in units (whether in, ft, m, etc...)

areas are in units² (in², ft², m², etc..., all squared units), and

volumes are in units³ (in³, ft³, m³, etc..., all cubed units).

 

Since the problem starts with squared units, and I am trying to get to cubed units, I will have to square root the values with squared units to bring them down to 'length values', and then cube those values to bring them to volume.

 

Combine the above background with setting up a proportion, since we are dealing with similar solids, and we get:

[√(356)³ / √(1058)³] = [x / 1754].

 

After cross multiplying and dividing, you should get

x ≈ 342.355 yd³