CK-12 Foundation
Volume by Cross Section: Volume of the Cone
Discover another way to find the volume of a cone. Pupils explore how the area of a cross section changes as it moves through a cone. The interactive uses that knowledge to develop the integral to use to find the volume of the cone....
Curated OER
Cross Sections and Collision Times
High schoolers solve five problems including finding the cross sectional area of two bodies, determining the swept out volume of a moving body, finding the average particle volume of a body and determining the collision time for a body.
Illustrative Mathematics
Use Cavalieri’s Principle to Compare Aquarium Volumes
Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required. From calculating the volume of a composite shape through the abstract...
EngageNY
General Prisms and Cylinders and Their Cross-Sections
So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the lesson develops the definition of a general cylinder. Scholars continue on to develop a graphical organizer for the...
EngageNY
The Volume of Prisms and Cylinders and Cavalieri’s Principle
Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not...
EngageNY
Volume and Cavalieri’s Principle
Take a slice out of life. The ninth section in a series of 23 introduces classmates to Cavalieri's principle using cross sections of a cone and stacks of coins. Class members participate in a discussion using pyramids and how Cavalieri's...
Mathed Up!
Volume of Prism
The area is essential to volume. As part of the review for the General Certificate of Secondary Education math assessment, a helpful video covers how to find the volume of several common 3-D figures. Pupils use the general volume formula...
EngageNY
End-of-Module Assessment Task - Geometry (module 3)
It's test time! Determine your class's understanding of the topics of volume and cross sections with a thorough assessment on volume, area, and geometric shapes.
Houston Area Calculus Teachers
Area and Volume
An AP calculus lesson begins with an activity to determine the volume of a solid using a cross-section. Next, learners review the ways to find the area between two curves , as well how to find the volume of a solid created from the...
CK-12 Foundation
Volume by Disks: The Vase Case
Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...
HeyMath!
Volume of Pyramid
Go beyond the basic formulas and uncover the surface area and volume of 3-D shapes with this comprehensive and organized worksheet packet. The problems include the basic formula computations while also challenging your learners to derive...
Rice University
Calculus Volume 3
See calculus to the end. The eBook is the last of a three-volume series covering college-level calculus topics. Scholars begin with parametric equations and polar coordinates before moving to vectors, finally ending with multi-variable...
EngageNY
The Volume Formula of a Pyramid and Cone
Our teacher told us the formula had one-third, but why? Using manipulatives, classmates try to explain the volume formula for a pyramid. After constructing a cube with six congruent pyramids, pupils use scaling principles from previous...
EngageNY
The Volume Formula of a Sphere
What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a...
University of Utah
Geometry Part 2: Measurement in 2- and 3-Dimensions, Plane Sections of Solids
What kind of tree does a math teacher climb? A geometry! Here is a lesson that includes all the geometry resources you could ever wish for in one comprehensive workbook. Class members demonstrate what they have learned by determining the...
Mathematics Vision Project
Module 5: Modeling with Geometry
Solids come in many shapes and sizes. Using geometry, scholars create two-dimensional cross-sections of various three-dimensional objects. They develop the lesson further by finding the volume of solids. The module then shifts to finding...
Mathematics Vision Project
Module 7: Modeling with Geometry
Model good modeling practices. Young mathematicians first learn about cross sections and solids of revolution. They then turn their attention to special right triangles and to the Laws of Sine and Cosine.
Virginia Department of Education
Exploring 3-D Geometry
Take young mathematicians on an exploration of the world of 3-D geometry with this seven-lesson unit. After first defining the terms perimeter, area, and volume and how they apply to the real world, students continue on to learn the...
Concord Consortium
Maximum Volumes
It's great to have a large swimming pool. An interesting performance task asks learners to optimize the volume of pools for a given surface area. They consider four different shapes for pools and find the maximum volume for each pool.
Curated OER
The Pyramid: Estimating Volumes
In this estimating volumes worksheet, students determine the area and volume of pyramids. They draw a cross-section of the pyramid. This four-page worksheet contains approximately 20 problems.
Mathematics Assessment Project
Fearless Frames
Show class members how to connect algebra to geometry. A high school assessment task has pupils determine volumes of two different containers given limitations on material for box frames. Pupils then write a paragraph on advice people...
College Board
2009 AP® Calculus AB Free-Response Questions Form B
Get a free peek into a calculus exam. Released free-response items from the AP® Calculus AB exam provide teachers and pupils examples of how topics may appear. The six questions cover topics such as growth rates, volumes of rotations,...
Resources for Educators
Fractions of Fun
Reinforce concepts and encourage learner engagement with a collection of math games, science experiments, and cross curricular activities. In one fun resource, learners sort objects, keep a diary of everyday fractions, play a game using...
Curated OER
Worksheet 2 - Spring 1996
In this math worksheet, students state the two fundamental laws of Calculus. Then they investigate finding the area of a rock in cross-sectional pieces.