a In similar solids, the corresponding linear measures have equal ratios. The common ratios are called the scale factor.
B
b Begin by finding the width and depth of the larger suitcase.
A
a 4:5
B
b 168 539.0675 cm^3
Practice makes perfect
a We have two suitcases that are similar rectangular prisms. We have been told that the smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep. The larger suitcase is 85 centimeters long, and we will let w and d be its width and depth, respectively.
We will find the scale factor of the prisms. In similar solids, the corresponding linear measures have equal ratios. The common ratios are called the scale factor. In this case, the ratio of the heights will give us the scale factor.
Scale Factor
68/85=4/5 ⇔ 4:5
The scale factor of the prisms is 4:5.
b To find the volume of the larger prism we should find its width and depth. We will first write a proportion using the scale factor to find its width.
The width of the larger suitcase is 58.75 centimeters. Proceeding in the same way, we will also find its depth.
4/5=27/d ⇔ d=33.75 cm
Now that we found the dimensions of the larger suitcase, we can find its volume. The volume of a rectangular prism can be found by multiplying its dimensions.
