Similar Solids: Definition, Properties, Area & Volume


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question 1 of 3

A sphere has a radius of 3 inches. If a similar sphere is to be created with a volume 8 times greater, what is the radius of the new sphere?

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1. A cube has a surface area of 24 square cm. If a similar cube is constructed with four times the surface area. How many times longer are the sides of the new cube compare to the original cube?

2. The surface area of a sphere is 4 square feet. A similar sphere is constructed with surface are 36 square feet. How many times larger is the new volume?

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About This Quiz & Worksheet

Put your knowledge of similar solids to the test with this quiz and worksheet. Questions will ask you to apply your knowledge to a series of practice problems.

Quiz & Worksheet Goals

In this set of questions, you'll test your understanding of:

  • The relationship between radius and volume
  • How the length of a cube's sides relates to its surface area
  • How to use the volume of a cylinder to find its height

Skills Practiced

This quiz and worksheet will allow students to test the following skills:

  • Making connections - use understanding of the concepts of radius and volume to find the radius for related spheres
  • Problem solving - use acquired knowledge to solve surface area and length-of-side practice problems
  • Knowledge application - use your knowledge to answer questions about how cones with different heights but similar sizes would relate their radii

Additional Learning

If you want to find out more about the relation between solids like this, read the lesson titled Similar Solids: Definition, Properties, Area & Volume. Concepts covered will include:

  • Real-world examples of how these formulas are applied
  • The defining dimensions of different shapes
  • What the 'orange slice' of a map is called