# Calculus AB: Use Basic Equations to Determine the Volume of a Solid (Cylinder)

## Overview

**Student will be able to use integration and differentiation to determine the volume of a solid and see the connection to the formula of a cylinder. **

# Instructor Directions

## Project Description | |

Name of Project | Use Basic Equations to Determine the Volume of a Solid (Cylinder) |

Subject Area | AP Calculus AB |

Targeted Standards | EU 3.4 The definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation. LO 3.4D Apply definite integrals to problems involving area, volume. |

Driving Question / Problem / Activator | What shape would be created when you rotate a rectangle around a given axis? What equations and constraints would allow you to determine the volume of a rectangle rotated around the x-axis? |

Project Summary | Student will be able to use integration and differentiation to determine the volume of a solid and see the connection to the formula of a cylinder. |

Estimated Time | 20-30 minutes |

Materials / Resources (including link to slideshow if available) | Graph PaperColored PencilsCalculator3-D Printer |

Tags | |

## Project Outline | |

Ask | What would be the volume of rectangle rotated around a fixed line? |

Imagine | What shape would be created when we rotate a rectangle around a fixed line? |

Plan | Draw a model of the imagined figure and determine how to find its volume. |

Create | Create a model of the figure using graph paper and the equation(s) to find the volume. |

Improve | |

Closure / Student Reflections | Connect the formula of a cylinder to the equation(s) you used to determine the volume. |

Possible Modifications / Extensions | Use a 3-D software program to create the solid being discussed. |

## Evaluation (Pre/Post)

*Insert Links to Google Forms*

Pretest Link: Evaluating Definite Integrals

Post-test Link: Using and Applying

## Credits or Modified From

## Additional Resources / Help for teaching this lesson

Students graph y=0

y=3

x=0

x=4 this will create the rectangle

Rotate the rectangle around the x-axis.

Have students discuss the resulting solids shape.

Determine the integral and constraints needed and evaluate the volume of the resulting solid.

Discuss the relationship of the integrated results and the formula for volume of a cylinder.

## Sample Pictures / Video