Exercise 1 Page 867

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of corresponding linear dimensions of two similar solids is the scale factor. With this in mind, we will consider the given cones to determine whether they are similar or not.

Let's see whether the corresponding linear dimensions are proportional.

4/3 ? =14/10.5

ExpandFrac

a/b=a * 10/b * 10

4/3 ? =140/105

ReduceFrac

a/b=.a /35./.b /35.

4/3 = 4/3 ✓

Since the corresponding linear dimensions are proportional, the cones are similar. The scale factor is 4:3. Since the sides have different lengths, the solids are not congruent.