MAFS.912.G-GMD.1.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

  • Assessment Limits :
    Items may require the student to recall the formula for the volume of
    a sphere.

    Items may require the student to find a dimension.

    Items that involve cones, cylinders, and spheres should require the
    student to do more than just find the volume.

    Items may include composite figures, including three-dimensional
    figures previously learned.

    Items may not include oblique figures.

    Items may require the student to find the volume when one or more
    dimensions are changed.

    Items may require the student to find a dimension when the volume
    is changed.

  • Calculator :

    Neutral

  • Clarification :
    Students will use volume formulas for cylinders, pyramids, cones, and
    spheres to solve problems
  • Stimulus Attributes :
    Items must be set in a real-world context.

    Items may require the student to apply the basic modeling cycle

  • Response Attributes :
    Items may require the student to use or choose the correct unit of
    measure.

    Items may require the student to apply the basic modeling cycle

Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question:

    A phosphate is mined, it moves along a conveyor belt, falling off of the end of the belt into the shape of a right circular cone, as shown.

    A shorter conveyor belt also has phosphate falling off of the end into the shape of a right circular cone. The height of the second pile of phosphate is 3.6 feet shorter than the height of the first. The volume of both piles is the same.

    To the nearest tenth of a foot, what is the diameter of the second pile of phosphate?

  • Difficulty: N/A
  • Type: EE: Equation Editor

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
2003390: Physics 1 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 and beyond (current))
2003836: Florida's Preinternational Baccalaureate Physics 1 (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-GMD.1.AP.3a: Use appropriate formulas to calculate volume for cylinders, pyramids, and cones.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 3 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Formative Assessments

Snow Cones:

Students are asked to solve a problem that requires calculating the volumes of a cone and a cylinder.

Type: Formative Assessment

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.

Type: Formative Assessment

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.

Type: Formative Assessment

Do Not Spill the Water!:

Students are asked to solve a problem that requires calculating the volumes of a sphere and a cylinder.

Type: Formative Assessment

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Volumes about Volume:

This lesson explores the formulas for calculating the volume of cylinders, cones, pyramids, and spheres.

Type: Lesson Plan

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.

Type: Lesson Plan

Cylinder Volume Lesson Plan:

Using volume in the real world

Type: Lesson Plan

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.

Type: Lesson Plan

Original Student Tutorial

I Scream! You Scream! We All Scream for... Volume!:

Have you ever ordered a scoop of ice cream in a cone and wondered how much ice cream actually fits inside the cone? By the end of this tutorial, you should be able to answer this question and solve other real-world problems by using the formula for the volume of a cone.

Type: Original Student Tutorial

Perspectives Video: Expert

Carbon Foam and Geometry:

Carbon can take many forms, including foam! Learn more about how geometry and the Monte Carlo Method is important in understanding it.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Volume and Surface Area of Pizza Dough:

Michael McKinnon of Gaines Street Pies explains how when making pizza the volume is conserved but the surface area changes.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Mathematically Optimizing 3D Printing:

Did you know that altering computer code can increase 3D printing efficiency? Check it out!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

KROS Pacific Ocean Kayak Journey: Food Storage Mass and Volume:

What do you do if you don't have room for all your gear on a solo ocean trek? You're gonna need a bigger boat...or pack smarter with math.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task

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.

Type: Unit/Lesson Sequence

Virtual Manipulative

Which Holds More? :

This interactive manipulative will let you compare and calculate volumes of different solids.

Type: Virtual Manipulative

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.

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

I Scream! You Scream! We All Scream for... Volume!:

Have you ever ordered a scoop of ice cream in a cone and wondered how much ice cream actually fits inside the cone? By the end of this tutorial, you should be able to answer this question and solve other real-world problems by using the formula for the volume of a cone.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

I Scream! You Scream! We All Scream for... Volume!:

Have you ever ordered a scoop of ice cream in a cone and wondered how much ice cream actually fits inside the cone? By the end of this tutorial, you should be able to answer this question and solve other real-world problems by using the formula for the volume of a cone.

Type: Original Student Tutorial

Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task

Virtual Manipulative

Which Holds More? :

This interactive manipulative will let you compare and calculate volumes of different solids.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Perspectives Video: Professional/Enthusiast

Estimating Oil Seep Production by Bubble Volume:

You'll need to bring your computer skills and math knowledge to estimate oil volume and rate as it seeps from the ocean floor. Dive in!

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

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.

Type: Problem-Solving Task

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).

Type: Problem-Solving Task