Key Concepts:
- Scaling Perimeter and Area in Similar Shapes: If all side lengths of a shape are scaled by a factor (k), the perimeter scales by k, the area scales by (k^2).
- Scaling Volume in 3D Similar Shapes: If all dimensions of a 3D shape are scaled by (k), the volume scales by (k^3).
Skills Covered:
- Calculating the area or volume of a shape, given the area or volume of a similar shape and the ratio of their side lengths.
- Given the area or volume of two similar shapes and the side lengths of one shape, calculating the side lengths of the other shape.
Example Problems:
- If the side length of a square doubles, how does its area change?
- If a circle’s radius triples, how many times larger is its area?
- If a cylinder has a volume of 64 and a height of 4, a similar cylinder has a volume of 1728, what is its height?