Matg Essay

4116 Words17 Pages
| Lesson 11: The Volume Formula of a Pyramid and Cone Student Outcomes Students use Cavalieri’s principle and the cone cross-section theorem to show that a general pyramid or cone has volume 13Bh, where B is the area of the base and h is the height by comparing it with a right rectangular pyramid with base area B and height h. Lesson Notes The Exploratory Challenge is debriefed in the first discussion. The Exploratory Challenge and Discussion are the springboard for the main points of the lesson: (1) explaining why the formula for finding the volume of a cone or pyramid includes multiplying by one-third and (2) applying knowledge of the cone cross-section theorem and Cavalieri’s principle from previous lessons to show why a general pyramid or cone has volume 13area of baseheight. Provide manipulatives to students, 3 congruent pyramids and 6 congruent pyramids, to explore the volume formulas in a hands-on manner; that is, attempt to construct a cube from 3 congruent pyramids or 6 congruent pyramids such as in the image below. Classwork Exploratory Challenge (5 minutes) Exploratory Challenge * Use the provided manipulatives to aid you in answering the questions below. a. i. What is the formula to find the area of a triangle? A=12bh ii. Explain why the formula works. The formula works because the area of a triangle is half the area of a rectangle with the same base and same height. * b. iii. What is the formula to find the volume of a triangular prism? For base area B and height of prism h, V=Bh. * iv. Explain why the formula works. A triangular prism is essentially a stack of congruent triangles. Taking the area of a triangle, repeatedly, is like multiplying by the height of the prism. Then the volume of the prism would be the sum of the areas of all of the congruent triangles, which is

    More about Matg Essay

      Open Document