R and S are two similar cuboids. The surface area of cuboid S is 107.5cm^2. Work out the surface area of cuboid R.

Question

the far back vertical line of R is: 2cm

the far back vertical line of S is: 5cm

Answer 1

First, you have to find the scale factor R/S based on the far back vertical lines = 2/5. (make sure the units are the same)

 

Then, because you are finding area, you must square the ratio: 2²/5² = 4/25   (For volume, you cube the ratio)

 

Now use that new ratio to set up a proportion with the surface area of S and solve for x: 4/25=x/107.5 

 

Cross multiply and set equal: 25x=4(107.5), now use simple algebra to solve for x

 

25x=430,  x=430/25,  x=17.2cm²