GEOM.MATH.11.D

Apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.

Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
formulasvolumethree-dimensional figuresprismspyramidsconescylindersspherescomposite figuresproblemsunits of measure
Skills
  • apply (formulas for volume) #dok2
  • determine (volume of three-dimensional figures) #dok2
  • solve (problems involving volume using appropriate units) #dok2
  • identify (three-dimensional figures and their relevant formulas) #dok1
  • analyze (composite figures to select and apply correct volume formulas) #dok3
Learning Targets
  • I can identify three-dimensional figures such as prisms, pyramids, cones, cylinders, spheres, and composite figures. #dok1
  • I can recall and write formulas for the volume of prisms, pyramids, cones, cylinders, and spheres. #dok1
  • I can determine which volume formula is appropriate for a given three-dimensional figure. #dok2
  • I can apply the correct formula to calculate the volume of a single three-dimensional figure. #dok2
  • I can solve problems involving the volume of composite figures by breaking them into simpler parts. #dok3
  • I can analyze a real-world scenario to choose the proper formulas and accurately compute total volume with the correct units. #dok3
Big Ideas
  • Volume formulas allow us to calculate the space occupied by three-dimensional objects in both mathematical and real-world contexts.
  • Understanding and applying the correct volume formulas is essential for interpreting and solving a wide variety of geometric problems.
Essential Questions
  • How do I determine which volume formula to use for a given three-dimensional figure?
  • Why is it important to use appropriate units of measure when calculating volume?
  • How can composite figures be decomposed so their total volume can be found?
  • In what real-world contexts might you need to calculate the volume of a three-dimensional object?
  • What strategies can help avoid common mistakes when applying volume formulas?