Course 3 Online!
Henrico County Public Schools, Virginia
8.7 - Surface Area & Volume
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Measurement
Focus: Problem Solving


The student will
a)   investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and
b)   describe how changing one measured attribute of a figure affects the volume and surface area. 
Essential Knowledge and Skills 
  • Distinguish between situations that are applications of surface area and those that are applications of volume.
  • Investigate and compute the surface area of a square or triangular pyramid by finding the sum of the areas of the triangular faces and the base using concrete objects, nets, diagrams and formulas.
  • Investigate and compute the surface area of a cone by calculating the sum of the areas of the side and the base, using concrete objects, nets, diagrams and formulas.
  • Investigate and compute the surface area of a right cylinder using concrete objects, nets, diagrams and formulas.
  • Investigate and compute the surface area of a rectangular prism using concrete objects, nets, diagrams and formulas.
  • Investigate and compute the volume of prisms, cylinders, cones, and pyramids, using concrete objects, nets, diagrams, and formulas.
  • Solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids.
  • Compare and contrast the volume and surface area of a prism with a given set of attributes with the volume of a prism where one of the attributes has been increased by a factor of 2, 3, 5 or 10.
  • Describe the two-dimensional figures that result from slicing three-dimensional figures parallel to the base (e.g., as in plane sections of right rectangular prisms and right rectangular pyramids).†Revised March 2011
Essential Understandings
  • How does the volume of a three-dimensional figure differ from its surface area? Volume is the amount a container holds. Surface area of a figure is the sum of the area on surfaces of the figure.
  • How are the formulas for the volume of prisms and cylinders similar? For both formulas you are finding the area of the base and multiplying that by the height.
  • How are the formulas for the volume of cones and pyramids similar? For cones you are finding 1/3 of the volume of the cylinder with the same size base and height. For pyramids you are finding 1/3 of the volume of the prism with the same size base and height.
  • In general what effect does changing one attribute of a prism by a scale factor have on the volume of the prism? When you increase or decrease the length, width or height of a prism by a factor greater than 1, the volume of the prism is also increased by that factor.
Vertical Articulation
  1. SOL 6.9 - make ballpark comparisons between U.S. Cust/metric system
  2. SOL 7.5abc - a) describe volume/surface area of cylinders; b) solve practical problems involving volume/surface area of rect. prims and cylinders; c) describe how changes in measured attribute affects volume/surface area
Instructional Materials
  1. Enhanced Scope and Sequence Lesson: Volume and Surface Area  (PDF) - Solving problems involving volume and surface area (Word)
  2. Notes: Surface Area and Volume (ppt)
  3. Notes: Surface Area and Volume #2 (ppt)
  4. Activity: Changing Attributes - Surface Area and Volume (pdf)
  5. VDOE Algebra Readiness Curriculum Companion: 3-D Geometry (pdf)
Real World Lessons
  1. Dan Meyer: You Pour, I Choose - Which glass contains more soda?
  2. Dan Meyer: Ticket to Ride - How many tickets are on the roll?
  3. Dan Meyer: Ditch Diggers - Guess whether or not the two ditch diggers will meet.
Practice
  1. Worksheet: Surface Area and Volume Word Problems #1 (doc)
  2. Worksheet: Surface Area and Volume Word Problems #2 (doc)
  3. Worksheet: Surface Area and Volume Word Problems #3 (doc)
  4. Worksheet: Surface Area and Volume Practice #1 (doc)
  5. Worksheet: Surface Area and Volume Practice #2 (doc)
  6. Worksheet: Surface Area and Volume Review (doc)
  7. Worksheet: Surface Area Practice (pdf)
  8. Quiz: Volume and Surface Area of 3-D Figures (doc)
Self-Assessments
  1. SOL 8.7a Mini-Quiz: Volume and Surface Area
  2. SOL 8.7b Mini-Quiz: Changes in Attributes
Skills
  1. Mathematics Assessment Project:
    • A18:Matchsticks - Apprentice - How many matchsticks can be made from a tree with a trunk with a base radius of 1 foot and a height of 80 feet?
    • E16:Propane Tanks - Expert - In this task, you must work out how much you need to change the radius of a propane gas tank in order to double its capacity.
  2. Practical Problem: Postal Expenses (doc)
Videos
Explore Learning
  1. Prisms and Cylinders - Activity A: Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder.
  2. Pyramids and Cones - Activity A: Vary the height and base‑edge or radius length of a pyramid or cone and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone.
  3. Surface and Lateral Area of Prisms and Cylinders: Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
  4. Surface and Lateral Area of Pyramids and Cones: Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
Websites
  1. Learn Alberta: Exploring Surface Area, Volume, and Nets (Object Interactive)
VDOE Interventions
  1. VDOE Algebra Readiness Curriculum Companion: Exploring 3-D Geometry - The lessons focus on the geometry and measurement of three-dimensional figures including surface area and volume of prisms, cylinders, cones and pyramids. Students will investigate and describe how changing the measure of one attribute affects the volume and surface area.(pdf)
  2. VDOE Algebra Readiness Curriculum Companion: – Investigating Patterns, Functions, and Algebra - (SOL 8.7a) The lessons focus on algebraic reasoning. Students explore the relationships found in number patterns through arithmetic and geometric sequences using variables expressions. They use modeling to collect data, and they learn to record data so that they can see the relationship that exists among tables, graphs, words, and equations. (pdf)
Common Core Standards
7.G.3
8.G.9
G-GMD.1
G-GMD.3
G-GMD.4
G-MG.1
G-MG.2
G-MG.3