Copy of 11.2 & 12.3 Ratios of Perimeters, Areas, and Volumes
Something that may help you understand and remember how to find the ratios of perimeters, areas, and volumes of similar and non-similar figures.
(Since areas of figures can be broken down into a bunch of squares/portions of squares and volumes of figures can be broken down into a bunch of cubes/portions of cubes, you can think about how the result would extend to more general figures).
2D Figure
original perimeter = 4
original area = 1
3D Figure
original base perimeter = 4
original base area = 1
original lateral area = 4
original surface area = 6
original volume = 1
(1) Slide k, the scale factor. Calculate the ratios of the various perimeters, areas, and volumes. Compare your answers to the answers on the worksheet.
(2) Uncheck "Change scale factor" and check "Change dimensions separately."
Keep two of the dimensions constant. Change only one of them (either , , or ). Calculate the ratios of the various perimeters, areas, and volumes. Compare your answers to the answers on the worksheet. For the 2D figure, what do you notice about the ratio of the areas? For the 3D figure, what do you notice about the ratio of the volumes?
Change , , and/or . Calculate the ratios of the various perimeters, areas, and volumes. Compare your answers to the answers on the worksheet. Notice that you can not easily write the ratios in terms of just , , or .