Similarity of solids - practice problems
Similarity of bodies explores the relationships between three-dimensional geometric shapes that have the same form but different sizes. Two bodies are similar when all corresponding linear dimensions are proportional by the same ratio, known as the scale factor. The concept is fundamental in understanding how volume and surface area scale with size changes. Applications include architectural modeling, map scaling, and understanding how physical properties change with size. Students learn to calculate missing dimensions, surface areas, and volumes of similar solids. This topic builds on two-dimensional similarity concepts and extends them into spatial reasoning.Instructions: Solve each problem carefully and provide a detailed solution for every item.
Number of problems found: 3
- Scale model
In a model train set, 1.38 inches represents one foot in real life. The height of One World Trade Center in New York City is 1776 feet. How tall would a scale model of the building be? Should you calculate 1776 x 1.38 or 1776 ÷ 1.38? - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums? - Two pots
Two similar pots have 16 cm and 10 cm heights if the smaller pot holds 0,75 l. Find the capacity of the larger pot
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