The volumes of two similar solids are 729 and 125. This means that the two 3-dimensional objects are geometrically similar, meaning they have the same shape, but not necessarily the same size. Specifically, the two objects have the same angles and lengths of sides, but the lengths of the sides are different. The volume of each is determined by the length of the sides and the shape itself.

## Understanding Volume

The volume of a 3-dimensional object is defined as the amount of space it occupies in a given area. It is calculated using the formula V = S x L x H, where S is the surface area, L is the length, and H is the height. Volume is usually expressed in cubic units such as liters, milliliters, or cubic meters. The units used to measure volume depend on the size of the object or the number of dimensions it has.

## Why Similar Solids Have Different Volumes

Two similar solids have the same shape, but different sizes. This is because the length of the sides of the solids changes. For example, if the sides of one solid are twice as long as the sides of the other solid, then the volume of the first solid will be eight times the volume of the second solid. This is because volume is proportional to the cube of the length of the sides. Thus, two similar solids can have different volumes even though they have the same shape.

## How to Calculate Volume

Calculating the volume of a 3-dimensional object is a relatively simple process. First, measure the length, width, and height of the object. Then, multiply the three measurements together. This will give you the volume of the object in cubic units. For example, if the length is 5 cm, the width is 4 cm, and the height is 3 cm, then the volume of the object is 5 x 4 x 3 = 60 cm3.

## Conclusion

The volumes of two similar solids are 729 and 125. This is because the lengths of the sides of the objects are different, even though they have the same shape. Volume is proportional to the cube of the length of the sides, so two similar objects can have different volumes. Calculating the volume of a 3-dimensional object is a simple process that involves measuring the length, width, and height of the object and multiplying them together.

The volumes of two similar solids are 729 and 125, due to differences in the lengths of the sides of the objects. Volume is proportional to the cube of the length of the sides, and can be calculated by multiplying the length, width, and height of the object. Understanding this relationship between similar solids and their volumes can help in many geometry and physics applications.