Unit Overview Cylinders and Cones and Spheres! Oh my! Grade 8, Unit 6

Cylinders and Cones and Spheres! Oh my! The Driving Questions for this Unit: How can you use what you already know about circles, prisms and pyramids to find the volumes of cones, cylinders and spheres? How can you use your knowledge about volumes of cones, cylinders and spheres to solve practical and mathematical problems? Why is the study of cones, cylinders and spheres so important?

Cylinders and Cones and Spheres! Oh my! Did you know that Ancient Greeks made connections between Geometry and real life contexts such as architecture? In fact, the field of Geometry played an important role in the development of mathematics as we know it today. In particular, so important was the relationship among cones, cylinders and spheres to the great mathematician Archimedes that a sphere and cylinder are displayed on his tombstone. Furthermore, in order to find the area of a circle, the Greek Mathematician Eudoxus used sequences of regular polygons to progressively obtain better representations of a circle. By using the known area of each regular polygon, he was able to squeeze out a good approximation for the area of a circle. He used similar methods to approximate volumes of three-dimensional shapes.

Cylinders and Cones and Spheres! Oh my! Eudoxus’ method, used to estimate areas and volumes, underpins the concept of a limit which is studied in Calculus. Calculus is fundamental to the work of the Scientists, Engineers and Mathematicians of today and the comparison of the attributes of cones, cylinders and spheres to volumes of rectilinear and curvilinear shapes is typically studied in a foundational Calculus course.

Cylinders and Cones and Spheres! Oh my! Knowing how to find or estimate the volumes of cones, cylinders and spheres is needed in many job settings. For example, examining how a container’s size and shape influences the volume of a product being sold is an important concept in Business and Marketing. Farmers on crop farms produce the grains, fruits, and vegetables that feed the country and they must understand volume in order to know how best to store and later package their crops.