Explain and use formulas for lateral area, surface area, and volume of solids.
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
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
Date of Last Rating: 06/07
Status: State Board Approved
Assessed: Yes


Example:  A gold class ring is dropped into a glass that is a right cylinder with a 6 cm diameter. The water level rises 1 mm. What is the volume of the ring?  Example:  Given the composite solid consisting of a hemisphere and a cone, calculate the surface area and the volume.


  • Reporting Category: Geometry
  • Item Type(s): This benchmark will be assessed using: MC , FR item(s)
    Also Assesses:

    MA.912.G.7.4 Identify chords, tangents, radii, and great circles of spheres.

    MA.912.G.7.6 Identify and use properties of congruent and similar solids.

  • Clarification :
    Students will explain and/or apply formulas to determine surface area, lateral area, and volume of solids.
  • Content Limits :

    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 ask students to apply knowledge of congruent and similar solids.

  • Stimulus Attributes :

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

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


  • Test Item #: Sample Item 1
  • Question:

    Abraham works at the Delicious Cake Factory and packages cakes in cardboard containers shaped like right circular cylinders with hemispheres on top, as shown in the diagram below.


    Abraham wants to wrap the cake containers completely in colored plastic wrap and needs to know how much wrap he will need. What is the total exterior surface area of the container?

  • Difficulty: N/A
  • Type: MC: Multiple Choice

  • Test Item #: Sample Item 2
  • Question:

    At a garage sale, Jason bought an aquarium shaped like a truncated cube. A truncated cube can be made by slicing a cube with a plane perpendicular to the base of the cube and removing the resulting triangular prism, as shown in the cube diagram below.


    What is the capacity, in cubic inches, of this truncated cube aquarium?

  • Difficulty: N/A
  • Type: FR: Fill-in Response