Focus

Math 10C Module 1 Lesson 6


This photo is of a castle.

© Jose Marines/shutterstock

How would you describe your favourite place to someone who has never been there? That place might be your bedroom at home, a cabin at the lake, or an ancient castle from your imagination. You could definitely use photos and drawings; but you also need a way to describe the size or dimensions of your place.

As you have been working on your math and spending time around your home and school, maybe you have noticed some basic geometric shapes in your environment. A single structure or space, such as the pictured castle, often includes a variety of geometrical shapes—prisms, pyramids, cones, cylinders, and spheres, for example.

If you have a structure that is made of more than one shape, how could you calculate its surface area and volume? What strategies can you develop to investigate the surface area and volume of complex shapes?

Outcomes

At the end of this lesson, you will be able to do the following:

  • Solve problems that involve surface area and the volume of 3-D objects.
  • Determine an unknown dimension of a right cone, cylinder, prism, pyramid, or sphere, given the object’s surface area or volume and the remaining dimensions.
  • Solve problems that involve surface area or volume, given a diagram of the composite 3-D object.
  • Describe the relationship between the volumes of right cones and cylinders with the same height and base and right pyramids and prisms with the same height and base.

Lesson Questions

  • Why is visualization important to the study of the surface area and volume of 3-D objects?
  • How does changing the dimensions of an object affect its surface area and volume?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.

** Note – Share questions may have to be done on your own depending on your learning situation**