Question

There are two similar purses. The blue purse has a volume of 837 cm? and the red purse has a volume of 248 cm3, If the width of the red purse is 15 cm, what is the width of the blue purse?

1. The width of the blue purse that is similar to the red purse is approximately 50.6 cm.

### How to Determine the Linear Measurement and Volume of Similar Solids?

If two solids, A and B, has a linear measure a and b respectively, and they are both similar to each other, the ratio of their volumes and their linear measures would be expressed as:
Volume of solid A/volume of solid B = a³/b³.
We are given two purses that are similar to each other:
Volume of Blue purse = 837 cm³
Volume of Red purse = 248 cm³
Width of Red purse = 15 cm
Let width of Blue purse be = x
Therefore we would have the following ratio:
Volume of blue purse/volume of red purse = (width of blue purse)³/(width of red purse)³
Plug in the values
837/248 = x/15
Cross multiply
(248)(x) = (837)(15)
248x = 112,555
Divide both sides by 248
248x/248 = 112,555/248
x = 50.6 cm
The width of the blue purse is approximately 50.6 cm.