MA.912.G.7.7Archived Standard

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Determine how changes in dimensions affect the surface area and volume of common geometric solids.

Remarks

Example: Explain how changing the radius or height of a cylinder affects its surface area and volume.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 2: Basic Application of Skills & Concepts
Standard: Polyhedra and Other Solids - Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids, and understand the properties of congruent and similar solids.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)
    • Also Assesses:

    MA.912.G.2.7 Determine how changes in dimensions affect the perimeter and area of common geometric figures.
  • Clarification :

    Students will determine how changes in parameter(s) affect perimeter, area, surface area, or volume, or vice-versa.

    Students will determine how changes to one parameter will change other parameters when the perimeter, area, surface area, or volume is held constant.

  • Content Limits :

    One or two parameters may be changed, resulting in the change of another parameter.

    Three parameters may be changed in one item only if all three are changed by a constant factor.

    Solids will be limited to right prisms, right circular cylinders, spheres, right pyramids, right circular cones, and/or composites of these solids.

    Items may not include oblique figures.

    Items may involve, explicitly and/or implicitly, no more than four parameters.

    Changes in dimension may or may not result in similar figures.

  • Stimulus Attributes :

    Items may be set in either mathematical or real-world contexts.

    Graphics should be used in most of these items, as appropriate.

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Kendra has a compost box that has the shape of a cube. She wants to increase the size of the box by extending every edge of the box by half of its original length. After the box is increased in size, which of the following statements is true?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: A city is planning to replace one of its water storage tanks with a larger one. The city’s old tank is a right circular cylinder with a radius of 12 feet and a volume of 10,000 cubic feet. The new tank is a right circular cylinder with a radius of 15 feet and the same height as the old tank. What is the maximum number of cubic feet of water the new storage tank will hold?
  • Difficulty: N/A
  • Type: FR: Fill-in Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plan

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

Student Resources

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