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Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★
Standard #: MAFS.912.G-GMD.1.3Archived Standard
Standard Information
General Information
Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Geometric Measurement & Dimension
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Explain volume formulas and use them to solve problems. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Related Courses
Related Resources
Formative Assessments
  • Snow Cones # Students are asked to solve a problem that requires calculating the volumes of a cone and a cylinder.
  • Sports Drinks # Students are asked to solve a problem that requires calculating the volume of a large cylindrical sports drink container and comparing it to the combined volumes of 24 individual containers.
  • The Great Pyramid # Students are asked to find the height of the Great Pyramid of Giza given its volume and the length of the edge of its square base.
  • Do Not Spill the Water! # Students are asked to solve a problem that requires calculating the volumes of a sphere and a cylinder.
Lesson Plans
  • Cape Florida Lighthouse: Lore and Calculations # The historic Cape Florida Lighthouse, often described as a conical tower, teems with mathematical applications. This lesson focuses on the change in volume and lateral surface area throughout its storied existence.
  • Yogurt Land Container # The student will assist Yogurt Land on choosing a new size container to offer their customers. The choice of containers are different three dimensional figures. Students will revisit the concepts of volume, surface area, and profit in order to make a decision. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
  • Evaluating Statements About Enlargements (2D and 3D) # This lesson is intended to help you assess how well students are able to solve problems involving area and volume, and in particular, to help you identify and assist students who have difficulties with the following:
    • Computing perimeters, areas and volumes using formulas.
    • Finding the relationships between perimeters, areas, and volumes of shapes after scaling.
  • Volumes about Volume # This lesson explores the formulas for calculating the volume of cylinders, cones, pyramids, and spheres.
  • The Cost of Keeping Cool # Students will find the volumes of objects. After decomposing a model of a house into basic objects students will determine the cost of running the air conditioning.
  • Cylinder Volume Lesson Plan # Using volume in the real world
  • Calculating Volumes of Compound Objects # This lesson unit is intended to help you assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties:
    • Computing measurements using formulas.
    • Decomposing compound shapes into simpler ones.
    • Using right triangles and their properties to solve real-world problems.
Original Student Tutorial
Perspectives Video: Expert
  • Carbon Foam and Geometry # <p>Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.</p>
Perspectives Video: Professional/Enthusiasts
Problem-Solving Tasks
  • Doctor's Appointment # The purpose of the task is to analyze a plausible real-life scenario using a geometric model. The task requires knowledge of volume formulas for cylinders and cones, some geometric reasoning involving similar triangles, and pays attention to reasonable approximations and maintaining reasonable levels of accuracy throughout.
  • Centerpiece # The purpose of this task is to use geometric and algebraic reasoning to model a real-life scenario. In particular, students are in several places (implicitly or explicitly) to reason as to when making approximations is reasonable and when to round, when to use equalities vs. inequalities, and the choice of units to work with (e.g., mm vs. cm).
Unit/Lesson Sequence
  • Three Dimensional Shapes # In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.
STEM Lessons - Model Eliciting Activity
  • Yogurt Land Container # The student will assist Yogurt Land on choosing a new size container to offer their customers. The choice of containers are different three dimensional figures. Students will revisit the concepts of volume, surface area, and profit in order to make a decision. Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
MFAS Formative Assessments
  • Do Not Spill the Water! # Students are asked to solve a problem that requires calculating the volumes of a sphere and a cylinder.
  • Snow Cones # Students are asked to solve a problem that requires calculating the volumes of a cone and a cylinder.
  • Sports Drinks # Students are asked to solve a problem that requires calculating the volume of a large cylindrical sports drink container and comparing it to the combined volumes of 24 individual containers.
  • The Great Pyramid # Students are asked to find the height of the Great Pyramid of Giza given its volume and the length of the edge of its square base.
Original Student Tutorials Mathematics - Grades 9-12
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