Lesson 15

Distinguishing Volume and Surface Area

Lesson Narrative

This is the first of two lessons where students apply their knowledge of surface area and volume to solve real-world problems. The purpose of this first lesson is to help students distinguish between surface area and volume and to choose which of the two quantities is appropriate for solving a problem. They solve problems that require finding the surface area or volume of a prism, or both. When they choose whether to use surface area or volume, they are choosing a mathematical model for the situation and engaging in MP4.

Learning Goals

Teacher Facing

  • Compare and contrast (orally and in writing) problems that involve surface area and volume of prisms.
  • Decide whether to calculate the surface area or volume of a prism to solve a problem in a real-world situation, and justify (orally) the decision.
  • Estimate measurements of a prism in a real-world situation, and explain (orally) the estimation strategy.

Student Facing

Let’s work with surface area and volume in context.

Required Preparation

Make 1 copy of the Card Sort: Surface Area or Volume blackline master for every 2 students, and cut them up ahead of time.

Learning Targets

Student Facing

  • I can decide whether I need to find the surface area or volume when solving a problem about a real-world situation.

CCSS Standards


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.
  • 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.

  • 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
  • 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.