### Examples

*Example*: A cylindrical swimming pool is filled with water and has a diameter of 10 feet and height of 4 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank to the nearest pound?

### Clarifications

*Clarification 1:*Instruction includes concepts of density based on volume.

*Clarification 2:* Instruction includes using Cavalieri’s Principle to give informal arguments about the formulas for the volumes of right and non-right cylinders, pyramids, prisms and cones.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Experts

## Perspectives Video: Professional/Enthusiasts

## Tutorial

## Unit/Lesson Sequence

## STEM Lessons - Model Eliciting Activity

Students use geometry formulas to solve a fruit growing company's dilemma of packing fruit into crates of varying dimensions. Students calculate the volume of the crates and the volume of the given fruit when given certain numerical facts about the fruit and the crates.

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.

In this activity, students will utilize measurement data provided in a chart to calculate areas, volumes, and densities of cookies. They will then analyze their data and determine how these values can be used to market a fictitious brand of chocolate chip cookie. Finally, they will integrate cost and taste into their analyses and generate a marketing campaign for a cookie brand of their choosing based upon a set sample data which has been provided to them.

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

Students are asked to solve a problem that requires calculating the volume of a sphere.

Students are asked to write the formula for the volume of a cone, explain what each variable represents, and label the variables on a diagram.

Students are asked to write the formula for the volume of a cylinder, explain what each variable represents, and label the variables on a diagram.

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

Students are asked to model a tree trunk with geometric solids and to use the model to estimate the volume of the tree trunk.

Students are asked to find the height of a square pyramid given the length of a base edge and its volume.

Students are asked to write the formula for the volume of a pyramid, explain what each variable represents, and label the variables on a diagram.

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

Students are asked to write the formula for the volume of a sphere, explain what each variable represents, and label the variables on a diagram.

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.

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.

Students are asked to derive and explain a formula for the volume of a cone given a pyramid with the same height and the same cross-sectional area at every height.

Students are asked to derive and explain a formula for the volume of a cylinder given a prism with the same height and the same cross-sectional area at every height.

Students are guided through the process of writing an informal argument for the volume of a pyramid formula using Cavalieri’s Principle.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

## Original Student Tutorials Mathematics - Grades 9-12

Learn to calculate the volume of a cone as you solve real-world problems in this ice cream-themed, interactive tutorial.

## Student Resources

## Original Student Tutorials

Learn how to calculate the volume of spheres while learning how they make Bubble Tea in this interactive tutorial.

Type: Original Student Tutorial

Learn to calculate the volume of a cone as you solve real-world problems in this ice cream-themed, interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

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!

Type: Perspectives Video: Professional/Enthusiast

## Tutorial

This video will show to find the volume of a triangular prism, and a cube by applying the formula for volume.

Type: Tutorial

## Parent Resources

## Perspectives Video: Professional/Enthusiast

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!

Type: Perspectives Video: Professional/Enthusiast