VOLUME OF CYLINDERS, SPHERES AND CONES

Investigation #1: Relationship between the volume of the cylinder and the sphere

Step #1: Carefully pour the rice from the original rice container into the cylinder until it is filled to the top. There is a rim around the cylinder that defines the top of the cylinder. Fill the rice to that rim only, not to the very tip of the actual cylinder. Pour out any excess rice from the original rice container into the bottom of the largest container where all the materials are stored. Don’t get rice on your desk!

Step #2: Pour the rice from the cylinder into the empty original rice container to proceed with the next step.

Step #3: This next step will have you pouring the rice from the cylinder into the sphere since the goal is to determine the relationship between the volume of the cylinder and the sphere. Instead of pouring the rice, you can use the spoon. The sphere does not have a removable base; therefore the hemisphere will be used. The hemisphere is one-half of the sphere, in other words, two hemispheres equal one sphere. The hemisphere has a removable base, so it is easier to bet the rice into it.

There is a rim around the hemisphere that defines the top of the hemisphere. Fill the rice to that rim only, not to the very tip of the actual hemisphere. After one of the hemispheres has been filled up to the rim, pour the rice from the hemisphere into the cylinder. Repeat this process a second time since two hemispheres of rice are necessary to replicate the amount of rice that can fill a sphere.

Step #4: Estimate the fraction of the cylinder that is filled with rice from the sphere.

The volume of the sphere = ______of the volume of the cylinder

Investigation #2: Relationship between the volume of the cylinder and the cone

Step #5:Dump the rice from the cylinder back into the original rice container.

Step #6:Pour or spoon the rice from the original rice container into the cone since the goal is to determine the relationship between the volume of the cylinder and the cone. There is a rim around the cone that defines the top of the cone. Fill the rice to that rim only, not to the very tip of the actual cone.

Step #7:Pour the rice in the cone back into the empty cylinder.

Step #8: Estimate the fraction of the cylinder that is filled with rice from the cone.

The volume of the cone = ______of the volume of the cylinder

Step #9:Pour all the rice back into the original rice container to pack away.

GLAnCE – 8th Grade – Session 4 – Exploring Volume and Surface Area- Participant Packet

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Grade 8: Presenter – Volume and Surface Area
Name of Activity / Description of Activity / Materials/Transparencies/
Handouts / Key Tips for the Teacher
Relationship of the volume of prisms to the area of the base times the height and the connection to the volume of cylinders /
  • Students will explore the relationship between the volume of prisms to the volume of cylinders. Emphasis will be made with the volume of prisms as the area of the base times the height or Bh. With this concept, the volume of cylinders will be explored.
  • Students will explore if volume is conserved.
/
  • Handout p 5
  • Rectangular Prisms
  • Overheads of Volume of Cylinders
  • Flat pattern of cylinder
  • Reeses Peanut Butter Cups
  • Card stock
/
  • Point out the importance of the conceptual development of volume and surface area. There is so much more to the instruction than just giving the students formulas.
  • It is crucial to the development of volume formulas that students do not learn volume as length x width x height. They tend to generalize this formula to all solids.
  • Students think that since area is conserved so is volume. They need concrete experiences first filling up a tall cylinder with candy and then a short cylinder, made from the same piece of tagboard. This helps to develop the mind set that the volumes are different before the mathematics is explored.

M-GLAnCE – 8th Grade – Session 4 – Exploring Volume and Surface Area – Facilitator Packet

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