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...
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...
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...
Virginia Department of Education
Surface Area and Volume
Partners use materials to wrap three-dimensional objects to determine the formula for surface area. The groups use an orange to calculate the amount of peel it takes to completely cover the fruit. Using manipulatives, individuals then...
EngageNY
Scaling Principle for Volumes
Review the principles of scaling areas and draws a comparison to scaling volumes with a third dimensional measurement. The exercises continue with what happens to the volume if the dimensions are not multiplied by the same constant.
Radford University
Fun with Solids
Cakes offer a yummy way to learn about math. Scholars use manipulatives to discover the formulas for the surface area and volume of prisms and cylinders. They use their formulas to calculate the amount of cake mix and frosting necessary...
Virginia Department of Education
Similar Solids and Proportional Reasoning
Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral...
Radford University
Building Sandcastles
Finalize the plans before playing in the sand. Learners design sandcastles using geometric and composite figures. They create blueprints, including the scale, and three-dimensional models of their castles. Finally, scholars calculate the...
NASA
The NBL Pool
That is a lot of water. Class groups explore the size of the NASA's Neutral Buoyancy Pool and calculate the volume of water needed to fill it. They then compare that volume to the amount of water needed to fill a pool the size of a...
Radford University
Down on Sue's Farm
When would a farmer use math? Class members work through five tasks on a farm that require knowledge of surface area, volume, and determining regression equations. The challenges range from figuring out the amount of paint to buy,...
Radford University
Fun with Solids
Geometry is all around us—if we're only willing to look. The final three activities of the Fun with Solids unit continue work on surface area and volume. For lesson three, scholars investigate the formulas for spheres and solve a problem...
Radford University
Ping Pong Packing
Bounce off some ideas to reduce the amount of wasted space. Teams work together to determine the best size and shape of container to package a large order of ping pong balls. Groups are to design the container to reduce the amount of...