http://www.ck12.org Chapter 11. Surface Area and Volume
Practice
Determine if each pair of right solids are similar. Explain
1.
2.
3.
4.- Are all cubes similar? Why or why not?
- Two prisms have a scale factor of 1:4. What is the ratio of their surface areas?
- Two pyramids have a scale factor of 2:7. What is the ratio of their volumes?
- Two spheres have radii of 5 and 9. What is the ratio of their volumes?
- The surface area of two similar cones is in a ratio of 64:121. What is the scale factor?
- The volume of two hemispheres is in a ratio of 125:1728. What is the scale factor?
- A cone has a volume of 15πand is similar to another larger cone. If the scale factor is 5:9, what is the volume
of the larger cone? - A cube has sides of lengthxand is enlarged so that the sides are 4x. How does the volume change?
- The ratio of the volumes of two similar pyramids is 8:27. What is the ratio of their total surface areas?
- The ratio of the volumes of two tetrahedrons is 1000:1. The smaller tetrahedron has a side of length 6 cm.
What is the side length of the larger tetrahedron? - The ratio of the surface areas of two cubes is 64:225. If the volume of the smaller cube is 13824m^3 , what is
the volume of the larger cube?
Below are two similar square pyramids with a volume ratio of 8:27. The base lengths are equal to the heights. Use
this to answer questions 16-21.
- What is the scale factor?
- What is the ratio of the surface areas?
- Findh,xandy.
- Findwandz.
- Find the volume of both pyramids.
- Find the lateral
Animal A and animal B are similar (meaning the size and shape of their bones and bodies are similar) and the
strength of their respective bones are proportional to the cross sectional area of their bones
- 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