How do you determine the volume of a similar shape?

To determine the volume of a similar shape, use the cube of the scale factor between the shapes.

When dealing with similar shapes, their corresponding dimensions are proportional. This means that if you have two similar shapes, the ratio of any pair of corresponding lengths (such as height, width, or depth) is the same. This ratio is known as the scale factor. For example, if one shape is twice as large as another in every dimension, the scale factor is 2.

To find the volume of a similar shape, you need to cube the scale factor. This is because volume is a three-dimensional measurement, and each dimension is scaled by the same factor. For instance, if the scale factor between two similar shapes is 3, then the volume of the larger shape is 3³ (which is 27) times the volume of the smaller shape.

Let's say you have a small cube with a volume of 8 cubic centimetres and a larger, similar cube with a scale factor of 2. To find the volume of the larger cube, you would calculate 2³, which equals 8. Then, multiply the volume of the smaller cube by this result: 8 cm³ × 8 = 64 cm³. Therefore, the volume of the larger cube is 64 cubic centimetres.

Understanding this principle is crucial for solving problems involving similar shapes, as it allows you to quickly and accurately determine the volume of one shape based on the volume of another.