Similar solids

Learning Objectives Define and identify similar solids. Determine the scale factor between two similar solids. Relate the scale factor to the ratio of corresponding linear dimensions. Apply the scale factor to find the ratio of surface areas of similar solids. Apply the scale factor to find the ratio of volumes of similar solids. Solve problems involving dimensions, surface areas, and volumes of similar solids. Explain real-world applications of similar solids. Have you ever seen a miniature replica of a famous building? 🗽 How do architects make sure the small model looks exactly like the real thing, just scaled down? In this lesson, you'll learn about similar solids, which are three-dimensional figures that have the same shape but different sizes. Understanding sim...

TermDefinitionExample Solid FigureA three-dimensional object that encloses a space. Examples include cubes, spheres, cylinders, and pyramids.A shoebox is a solid figure (a rectangular prism). Similar FiguresFigures that have the same shape but not necessarily the same size. All corresponding angles are equal, and all corresponding linear dimensions are proportional.Two squares of different side lengths are similar figures. Similar SolidsThree-dimensional figures that have the same shape but different sizes. All corresponding linear dimensions (like edges, heights, radii) are proportional.A small basketball and a large basketball are similar solids (spheres). Corresponding PartsMatching vertices, edges, faces, heights, or radii in similar solids. These parts hold the same relative position...

Scale Factor of Linear Dimensions $k = \frac{\text{linear dimension of Solid A}}{\text{linear dimension of Solid B}}$ To find the scale factor (k) between two similar solids, divide any linear dimension of the first solid by the corresponding linear dimension of the second solid. Make sure to be consistent with which solid is 'A' and which is 'B'. Ratio of Surface Areas of Similar Solids $\frac{\text{Surface Area of Solid A}}{\text{Surface Area of Solid B}} = k^2$ If two solids are similar with a scale factor of $k$, then the ratio of their surface areas is the square of the scale factor. This means if Solid A is $k$ times larger in linear dimensions, its surface area is $k^2$ times larger. Ratio of Volumes of Similar Solids $\frac{\text{Volume of S...