How changing dimensions affects perimeter, area, and volume

When every linear dimension of a figure is multiplied by a scale factor k, the new figure is similar to the original, and its measurements change in predictable ways: perimeter and other lengths are multiplied by k, area and surface area by k^2, and volume by k^3. Doubling the side of a cube doubles its edges, makes its surface area 4 times as large, and makes its volume 8 times as large. The reverse also works: if two similar figures have areas in a ratio of 9 to 1, their lengths are in a ratio of 3 to 1. A non-proportional change, where only some dimensions change, produces a figure that is not similar to the original, so the effects must be worked out from the formula: doubling only a cylinder's height doubles its volume, but doubling only its radius makes the volume 4 times as large, since volume depends on the radius squared.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report