Grade 8 Mathematics Module 7, Topic D, Overview

Girl Studying

In Topic D, students learn that radical expressions naturally arise in geometry, such as the height of an isosceles triangle or the lateral length of a cone.  The Pythagorean Theorem is applied to three-dimensional figures in Topic D as students learn some geometric applications of radicals and roots (8.G.B.7).  In order for students to determine the volume of a cone or sphere, they must first apply the Pythagorean Theorem to determine the height of the cone or the radius of the sphere.  Students learn that truncated cones are solids obtained by removing the top portion above a plane parallel to the base.  Students know that to find the volume of a truncated cone they must access and apply their knowledge of similar figures learned in Module 3.  Their work with truncated cones is an exploration of solids that is not formally assessed.  In general, students solve real-world and mathematical problems in three dimensions in Topic D (8.G.C.9).  For example, now that students can compute with cube roots and understand the concept of rate of change, students compute the average rate of change in the height of the water level when water is poured into a conical container at a constant rate.  Students also use what they learned about the volume of cylinders, cones, and spheres to compare volumes of composite solids.

Downloadable Resources

Resources may contain links to sites external to the EngageNY.org website. These sites may not be within the jurisdiction of NYSED and in such cases NYSED is not responsible for its content.

Common Core Learning Standards

CCLS State Standard
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world...
8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world...

Curriculum Map