Help please. The volumes of two similar solids are 1,331 cubic meters and 216 cubic meters. The surface area of the larger solid is 484 cubic meters. What is the surface area of the smaller solid?

Question

imstuck · Answer

In order to do this you have to find the similarity ratio so that when you set up your equation you are not dealing with meters cubed and meters squared.  The volume of a figure has units that are cubed, right?  So in order to find the similarity ratio, which is 1:1, you have to take the cubed root of both the numbers.  The cubed root of 1331 is 11 (you are allowed to do this on your calculator I hope?) and the cubed root of 216 is 6.  So the ratio of the larger to the smaller is 11:6.  Now they gave you a measurement of 484 which is the surface area of the larger solid. In order to find out what the surface area of the smaller is, you have to set up an equivalency statement with x (your unknown) as the surface area of the smaller solid.  Here's the equivalency statement:$$\frac{ 11 }{ 6 }=\frac{ 484 }{ x }$$Since you have the ratio from larger to smaller, you have to make sure you put the larger surface area on top, too.  x is the surface of the smaller solid, which you are going to solve for.  Cross multiplication works here giving you 11x = 484(6)-->11x = 2904.  Solving for x has you dividing both sides by 11:  x = 2904/11 which is 264.  That is the surface area of the smaller solid.  Just remember in a situation like this, solve for the similarity ratio first, then use what you have to find what you don't. Anything else you need help with?