Similar Solids (Jump to: Lecture | Video )

Figure 1.

The above two figures are similar solids. The scale of these two models is 1:3. The model on the right is three times as big as the model on the left.

That means that the surface area of these two models has a ratio of 1^2:3^2, which is 1:9.

Surface Area of Figure 1 = 2((2)(2) + (2)(5) + (2)(5)) = 48 square inches

Surface Area of Figure 2 = 48 * 9 = 432 square inches

It also means that the volumes of these two models has a ratio of 1^3:3^3, which is 1:27.

Volume of Figure 1 = (2)(2)(5) = 20 cubic inches

Volume of Figure 2 = 20 * 27 = 540 cubic inches