Math Units Page

Lesson Purpose

The purpose of this lesson is to expand student's knowledge of using the volume formulas.  Students will use volume formulas to calculate volume of cylinders, cones, and spheres as well as calculate missing dimensions for real-world problems.  Students will use these skills to determine the difference in volume of a rectangular shaped pool and a cylindrical shaped pool.  Also, student will look at the amount of space four ice cubes take up after melting into a cylindrical shaped container.  The ability to use and explain volume formulas is a major work for Level E Geometry.

Students will use many previously learned skills in this lesson in order to calculate volume and the missing dimensions when given volume.  Students will need to have an understanding of substitution and solving equations for a variable.  Students will also need to be familiar with converting units of measure.

Related Documents

Lesson Objectives

At the end of this lesson, students will be able to:

• use formulas to solve for problems involving volume of cylinders.
• use formulas to solve for problems involving volume of cones.
• use formulas to solve for problems involving volume of spheres.
• use formulas to solve for missing dimensions involving volume of cylinders, cones, and spheres.
• apply concepts of density in the context of area and volume.

Student Target

"I can use formulas to calculate

• the volume of a cylinder."
• the volume of a cone."
• the volume of a sphere."
• for the missing dimensions when given the volume."

"I can apply concepts of density for a given area or volume."

CCR Focus Standards

Geometry - Level D

Geometry - Level E

• G.GMD.3

  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

Supporting Standards

• 6.EE.7

  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
  

• G.CO.1

  Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  

Standards for Mathematical Practice

• MP.1

  Make sense of problems and persevere in solving them. (MP.1)

• MP.5

  Use appropriate tools strategically. (MP.5)

• MP.6

  Attend to precision. (MP.6)

KYAE Employability Standards

• E.1

  E.1 Effectively contribute to a team through cooperation, leadership, and giving and accepting critical feedback to work toward a common goal.

• E.5

  E.5 Utilize resources responsibly.

• E.7

  E.7 Accurately analyze information and respond appropriately.