Complete the fraction multiplication sentence

Learning Objectives Relate fractional scale factors to changes in length, surface area, and volume of 3D figures. Set up and complete fraction multiplication sentences to find unknown dimensions of similar solids. Use squared fractional scale factors to complete multiplication sentences for surface area ratios. Apply cubed fractional scale factors to complete multiplication sentences for volume ratios. Solve problems involving fractional parts of a 3D figure's properties by working backwards from area or volume ratios. Deconstruct a geometric word problem into a fraction multiplication sentence to find a missing value. Ever wonder how an architect's small model perfectly represents a giant skyscraper? 🏗️ It's all about scaling with fractions, a concept we&#039...

TermDefinitionExample Similar SolidsTwo three-dimensional figures are similar if they have the same shape and all their corresponding dimensions are proportional.A sphere with a radius of 2 cm is similar to a sphere with a radius of 5 cm. A cube with a side length of 3 inches is similar to a cube with a side length of 1 inch. Scale Factor (k)The constant ratio of corresponding linear dimensions (like height, radius, or side length) of two similar solids. It is often expressed as a fraction.If a large cone has a height of 15m and a similar small cone has a height of 10m, the scale factor from large to small is 10/15, which simplifies to k = 2/3. Linear DimensionA one-dimensional measurement of a figure, such as length, width, height, radius, or slant height. The ratio of corresponding line...

Surface Area Ratio Formula A_{new} = k^2 \cdot A_{original} = (\frac{a}{b})^2 \cdot A_{original} Use this formula to find the surface area of a similar solid. Multiply the original surface area by the square of the fractional scale factor (k = a/b). Volume Ratio Formula V_{new} = k^3 \cdot V_{original} = (\frac{a}{b})^3 \cdot V_{original} Use this formula to find the volume of a similar solid. Multiply the original volume by the cube of the fractional scale factor (k = a/b). Finding the Scale Factor from Ratios k = \sqrt{\frac{A_{new}}{A_{original}}} \quad \text{or} \quad k = \sqrt[3]{\frac{V_{new}}{V_{original}}} If you know the surface areas or volumes of two similar solids, you can find the linear scale factor by taking the square root of the area ratio or the cub...