9-3B Volume of Similar Solids What is the relationship between the similarity ratio of two similar solids and the volumes of those solids?

Similar Cylinders Are the cylinders similar? What is their similarity ratio? Find the volume of each cylinder. What is the ratio of their volumes? V = π(1) 2 3 V = 3π V = π(3) 2 (9) V = 81π

Similar Animals The weight of an object of a given density is proportional to its volume. Suppose the measurements of one animal are four times the measurements of another, and the two animals are geometrically similar. How many times greater is the weight of the larger animal than the weight of the smaller? Similarity ratio 4/1 V=(4) 3 =64

Two years ago, Josh bought a puppy that weighed 2 lb. Since then, it has tripled in length. About how much does the dog weigh now? The similarity ratio is 3/1. Ratio of the volumes would be (3/1) 3 = 27 Weight is proportional to volume, so the dog now weighs about 2 ×27 = 54 lbs

What is the ratio of the volumes of the two cubes shown? 20 cm 40 cm

The ratio of the volumes of two similar cylinders is 125/27. What is the ratio of their radii? ? ? Sim ratio Vol ratio

Suppose that two similar animals have a similarity ratio of 3/2. The smaller one weighs 10 lb. What does the larger one weigh? Volume

Similarity Ratio (any part) Surface Area Ratio Volume Ratio

Theorem The ratio of the volumes of two similar solids is the cube of their similarity ratio.

What is the relationship between the similarity ratio of two similar solids and the volumes of those solids? The similarity ratio is cubed to find the similarity ratio of the volumes.