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Gr. 8 Unit: 8.G.C.9: Volume of Cylinders, Cones, and Spheres

Lesson Seed C.9: Volume

Essential Questions:

What is the relationship between the volumes of cylinders, cones, and spheres?

What is the difference between volume and surface area of cylinders, cones, and spheres?

If congruent or similar plane figures are stacked, what kinds of solids are formed?

How do geometric models describe spatial relationships among the dimensions for cylinders, cones, and spheres?

How can volume formulas for cylinders, cones, and spheres be used to solve authentic problems in life?

Lesson Plans and Seeds

Lesson Plan C.9: Volume of Cylinders, Cones, and Spheres

Lesson Seed C.9: Volume

Download Seeds, Plans, and Resources (zip)

Unit Overview

Content Emphasis By Clusters in Grade 8

Progressions from Common Core State Standards in Mathematics

Send Feedback to MSDE’s Mathematics Team

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

Standard(s): 8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Purpose/Big Idea:

Conceptually understand the formula for volume of a cone/sphere

Materials:

Graph paper or grid
Clear cylinder
Clear cone having same base area and height as cylinder
Water tinted with food coloring (or rice)

Activity:
Exploration:

Cylinder
Show students how the clear base of the cylinder is covered with squares when placed on the grid (area of base). Then this is layered to the top of the cylinder (area of base times height—area of a circle base times the height or V = πr²h). Dropping sugar cubes in the cylinder is also a good visual.
Cone
Take the clear cone that has the same base area and height as the cylinder. Fill the cone with tinted water or rice. Ask students if they can guess the relationship between volume of the cylinder and the cone. After their discussion pour the water from the cone into the cylinder, showing the level to students. Ask if they need to adjust their hypothesis. Then show how many cones of water it takes to fill the cylinder.
Since it takes 3, they should visually see that the volume of the cone is 1/3 the volume of the cylinder. Volume of cone should now be visually seen as V = volume of cylinder. V = πr²h
Sphere
Show a picture of a sphere enclosed with a cylinder that has the same radius and height as the sphere.

Note: the height of the cylinder is twice the radius of the sphere. The radius is r, therefore the length of the base of the cylinder is 2r If the sphere is filled with liquid, it will fill of the cylinder. Use models to prove this. Volume of sphere = volume of a cylinder Volume of sphere: V = (πr²h) remember: the height is 2r so substitute this into the formula for height V = (πr²2r) V = (2r) πr² V = πr³

Guiding Questions:

How do the volumes of cylinders, spheres and cones relate to each other?

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Last Updated 3/9/2020 2:45 PM