Surface area and volume of similar solids

Learning Objectives Identify similar rectangular prisms based on their dimensions. Determine the linear scale factor between two similar rectangular prisms. Explain how the dimensions of a solid change when it is scaled by a given factor. Calculate the new surface area of a rectangular prism after it has been scaled by a linear factor. Calculate the new volume of a rectangular prism after it has been scaled by a linear factor. Use coordinates to describe the base of a rectangular prism and then apply scaling to its dimensions. Solve real-world problems involving the scaling of similar solids. Have you ever seen a small toy car and a real car that look exactly alike, just different sizes? 🚗 What makes them 'look alike' even though one is tiny and the other is hug...

TermDefinitionExample Solid FigureA three-dimensional shape that takes up space, like a cube or a rectangular prism.A shoebox is a solid figure, specifically a rectangular prism. Similar SolidsTwo solid figures are similar if they have the exact same shape but different sizes. All their corresponding lengths (like length, width, and height) are multiplied by the same number.A small cube and a large cube are similar solids because one is just a scaled-up version of the other. Scale Factor (Linear)The number by which all the dimensions (length, width, height) of a solid are multiplied to create a similar solid. It tells us how much bigger or smaller the new solid is in each direction.If a box is 2 inches long and a similar box is 4 inches long, the scale factor is 2 (because 2 x 2 = 4). Sur...

Scaling Dimensions of Similar Solids If a solid is scaled by a linear scale factor $k$, then its new dimensions are $k$ times its original dimensions. To find the new length, width, or height of a similar solid, multiply the original dimension by the scale factor $k$. For example, if original length is $L$, new length is $L' = k \times L$. Scaling Surface Area of Similar Solids If a solid is scaled by a linear scale factor $k$, its new surface area is $k^2$ times its original surface area. To find the new surface area of a similar solid, first find the original surface area, then multiply it by the square of the linear scale factor ($k \times k$). For example, if original surface area is $SA$, new surface area is $SA' = k^2 \times SA$. Scaling Volume of Similar...