11.9. Area and Volume of Similar Solids http://www.ck12.org
- What is the scale factor?
- What is the ratio of the surface areas?
- Findh,xandy.
- Findwandz.
- Find the volume of both pyramids.
- Find thelateralsurface area of both pyramids.
Animal A and animal B are similar (meaning the size and shape of their bones and bodies are similar) andthe
strength of their respective bones are proportional to the cross sectional area of their bones. Answer the following
questions given that the ratio of the height of animal A to the height of animal B is 3:5. You may assume the lengths
of their bones are in the same ratio.
- Find the ratio of the strengths of the bones. How much stronger are the bones in animal B?
- If their weights are proportional to their volumes, find the ratio of their weights.
Summary
This chapter presents three-dimensional geometric figures beginning with polyhedrons, regular polyhedrons, and an
explanation of Euler’s Theorem. Three-dimensional figures represented as cross sections and nets are discussed.
Then the chapter branches out to the formulas for surface area and volume of prisms, cylinders, pyramids, cones,
spheres and composite solids. The relationship between similar solids and their surface areas and volumes are
explored.
Chapter Keywords
- Polyhedron
- Face
- Edge
- Vertex
- Prism
- Pyramid
- Euler’s Theorem
- Regular Polyhedron
- Regular Tetrahedron
- Cube
- Regular Octahedron
- Regular Dodecahedron
- Regular Icosahedron
- Cross-Section
- Net