Lester is constructing two similar boxes shaped as similar rectangular prisms. The larger box has a height of 18 inches and a square base of side length 15 inches. If the smaller box has a height of 12 inches, what is its volume?

Question

Lester is constructing two similar boxes shaped as similar rectangular prisms. The larger box has a height of 18 inches and a square base of side length 15 inches.    If the smaller box has a height of 12 inches, what is its volume?

campbell_st · Answer

Large box  volume = V = 15^2 x 18

                                     V = 4050 inches^3

Small box since similar ratios are the same for all sides... 

12/18 = 2/3  the small box has measurements 2/3 the size of the large box

so the base lengths are  2/3 x 15 = 10

small box volume   V = 10^2 x 12 
                                 V = 1200 inches ^3

the alternative method is   (2/3)^3 x volume of the large box... 


                                        8/27 x 4050 = 1200 inches^3

since you are finding volume the scaling factor is cubed...
 
if it was area the scaling factor is squared. 

hope this helps