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.
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....
EngageNY
General Pyramids and Cones and Their Cross-Sections
Are pyramids and cones similar in definition to prisms and cylinders? By examining the definitions, pupils determine that pyramids and cones are subsets of general cones. Working in groups, they continue to investigate the relationships...
NASA
Next Generation Spacecraft—Orion
What is the cross-sectional area of the Orion spacecraft? Groups work together to estimate the area of a cross section of the Orion spacecraft by first counting the number of grids a scale drawing covers. Pupils also employ a method...
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...
Curated OER
Multi-dimensional Modeling of Ore Bodies Making Sense of Empirical Data
Math scholars identify four different rock types in that strata and use this identification and data to construct a two dimensional geologic cross-section. They use data tables to construct a three-dimensional geologic cross-section.
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...
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...
Curated OER
Challenge Sheet 7: Area and Cross-Sections
In this area worksheet, students set up integrals which evaluate the area of a region bounded by graphs. they use vertical and horizontal cross-sections. This two-page worksheet contains seven multi-step problems.
Curated OER
Measuring the Area of a Circle
When mathematical errors happen, part of the learning is to figure out how it affects the rest of your calculations. The activity has your mathematicians solving for the area of a circular pipe and taking into consideration any errors...
Curated OER
Surface Area of Prism
Tenth graders are provided instructions, including a video, on calculating the surface area of a prism. The one-page interactive worksheet contains two worked questions. Answers are included.
Curated OER
Area of Cross-Sections
In this area worksheet, students find the area of regions bounded by graphs. They set up integral equations for determining the vertical cross-section and the horizontal cross-section of a given figure. This one-page worksheet contains...
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.
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...
EngageNY
Unknown Length and Area Problems
What is an annulus? Pupils first learn about how to create an annulus, then consider how to find the area of such shapes. They then complete a problem set on arc length and areas of sectors.
Curated OER
Tree Cookies
You will find a viewer-friendly PowerPoint on the growth rings and other features found in a cross-section of a tree trunk, affectionately known as a "tree cookie." A few worksheets are provided for practice counting tree rings and a...
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...
Curated OER
Signs of Change: Tree Rings
Students identify and experiment with dendrochronology (the study of tree rings to answer ecological questions about the recent past) and come up with conclusions as to what possible climatic conditions might affect tree growth in their...
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...
Curated OER
Air Resistance and Friction
Physics learners experiment with three laboratory activities to learn about air resistance and friction. First, they use a hair dryer to move different sized spheres to determine the relationship between cross-sectional area and air...
Teach Engineering
Load It Up!
See how a marshmallow can hold up a bridge load. Teams take a closer look at the design of bridge piers. They determine the types of loads that might affect a bridge, and, using that information, they calculate the needed cross-sectional...
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...
Curated OER
Worksheet 2 - Spring 1996
For this math worksheet, students state the two fundamental laws of Calculus. Then they investigate finding the area of a rock in cross-sectional pieces.