Question

The ratio of the corresponding linear measures of two similar jewelry boxes is 2 to 3. The larger box has a volume of 162 cubic inches. What is the volume of the smaller jewelry box?

Answer 1

Hello welcome to QuestionCove o:
Personally how I would solve this question would to just divide 162 by 3, and then multiple by 2 to get the volume of the smaller box

Answer 2

the ratio of linear dimensions is not the same as the ratio of the volumes

to better understand this, consider a cube with side length 3 and volume s^3. increasing the dimension by a scale factor k results in the new volume being k^3 * s^3. therefore, the volume ratio is the cube of the linear ratio

since you have a 2:3 linear ratio, the volume ratio is 8:27 (2^3:3^3)

therefore:

(small box volume/large box volume) = (8/27)

solve for the volume of the small box