In this section, you will compare surface areas.

The surface area of 3-dimensional figures is affected the same way as the area is for 2-dimensional figures. The key is that dimensions are 1-dimensional and area is 2-dimensional. That is why you multiply the scale factors for the dimensions together when determining the scale factor for area.

Example

Consider the two boxes of cereal below. If the dimensions of the larger box were twice the dimensions of the smaller box, compare the amount of cardboard needed to make the boxes. Click on the cereal boxes to reveal the answer.

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Since surface area is still two dimensional, just take the square of the scale factor (in this case, “twice” (2) and you will see that the surface area of the larger box is four times (2 × 2) the surface area of the smaller box.