Lesson 18

The Volume and Dimensions of a Cylinder

Lesson Narrative

In this lesson students learn that the volume of a cylinder is the area of the base times the height, just like a prism. This is accomplished by considering 1-unit-tall layers of a rectangular prism side by side with 1-unit-tall layers of a cylinder. After thinking about how to compute the volume of specific cylinders, students learn the general formulas \(V=Bh\) and \(V=\pi r^2 h\).

In the warm-up, students recall that a circle’s area can be determined given its radius or diameter. Students also become familiar with what is meant by radius and height as those terms apply to cylinders. Next, students compute the volume of a cylinder by multiplying the area of its base by its height. Finally, students compute volumes given radius and height, and find radius or height given a cylinder’s volume and the other dimension by reasoning about the structure of the volume formula.


Learning Goals

Teacher Facing

  • Calculate the value of one dimension of a cylinder, and explain (orally and in writing) the reasoning.
  • Calculate the volume of a cylinder, and compare and contrast (orally) the formula for volume of a cylinder with the formula for volume of a prism.

Student Facing

Let’s explore cylinder volumes and dimensions.

Learning Targets

Student Facing

  • I can find missing information about a cylinder if I know its volume and some other information.
  • I know the formula for volume of a cylinder.

CCSS Standards

Building On

Addressing

Glossary Entries

  • base (of a prism or pyramid)

    The word base can also refer to a face of a polyhedron.

    A prism has two identical bases that are parallel. A pyramid has one base.

    A prism or pyramid is named for the shape of its base.

    Two figures, a pentagonal prism and a hexagonal pyramid.
  • cone

    A cone is a three-dimensional figure like a pyramid, but the base is a circle.

  • cross section

    A cross section is the new face you see when you slice through a three-dimensional figure.

    For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.

  • cylinder

    A cylinder is a three-dimensional figure like a prism, but with bases that are circles.

  • prism

    A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.

    Here are some drawings of prisms.

    A triangular prism, a pentagonal prism, and a rectangular prism.
  • pyramid

    A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.

    Here are some drawings of pyramids.

    a rectangular pyramid, a hexagonal pyramid, a heptagonal pyramid
  • sphere

    A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.

  • surface area

    The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.

    For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm2.

  • volume

    Volume is the number of cubic units that fill a three-dimensional region, without any gaps or overlaps.

    For example, the volume of this rectangular prism is 60 units3, because it is composed of 3 layers that are each 20 units3.

    Two images. First, a prism made of cubes stacked 5 wide, 4 deep, 3 tall. Second, each of the layers of the prism is separated to show 3 prisms 5 wide, 4 deep, 1 tall.

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