EM - Equations and Measurement Module Overview

Equations and Measurement Module Overview

image of a pizza (circle) with a slice cut out (triangle)Geometry is an integral part of everyday life. The shapes we study in Geometry are found all throughout nature, and in objects we see and use each day. We combine Algebra with Geometry to find the density of an object, to figure out how to maximize the volume of a container while minimizing cost, and to maximize the amount of area enclosed by a certain amount of fencing. When Algebra is combined with Geometry, the number of problems we can solve are almost limitless! 
We can answer questions like these.  How much ice cream does your waffle cone hold? How much oil can fit in each barrel? If you drink a full glass of water, how much did you drink? If you slice a pyramid horizontally at any point, what shape will you get? Believe it or not, these are all questions about area and volume that can be answered with the tools you will gain within this module!

Essential Questions

  • What is Cavalier's principle and how can we use it to find the volume of a cylinder, pyramid, cone, sphere, and other prisms?
  • How can we identify the shape of a cross section of a three-dimensional object?
  • What types of three-dimensional shapes can be created by rotating a two-dimensional object about an axis?
  • What shapes can we use to describe a variety of real life objects?
  • How can we apply the concept of density based on area and volume in real life situations?
  • How can we solve various design problems using geometric methods?

Key Terms

The following key terms will help you understand the content in this module.

Cone - a three-dimensional closed figure with circular base connected to a vertex.

Cylinder - is a three-dimensional closed figure with congruent, parallel bases connected by the set of all segments between the two circular bases.

Density - the mass of an object divided by its volume

Hemisphere - the half sphere formed by a plane intersecting the center of a sphere.

Polyhedron - a three-dimensional solid with flat polygon faces joined at their edges.

Prism - a polyhedron with two congruent faces, called bases, that lie on parallel planes. The other lateral faces that connect the bases are parallelograms.

Pyramid - a polyhedron with one base and lateral faces that are triangles.

Sphere - a set of points in three-dimensional space equidistant from a point called the center. 

Volume - the amount of 3 dimensional space an object occupies

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