Students must calculate the volume of a cone in this real world task.

This interactive exercise focuses on comparing volumes between figures that have the same height and diameter and drawing conclusions based on the ratios of the sizes.

The purpose of this task is to give students practice working the formulas for the volume of cylinders, cones and spheres, in an engaging context that provides and opportunity to attach meaning to the answers.

Explanation of surface area and the volume of pyramids, prisms, cylinders, and cones through examples and a video lesson. [1:44]

This task gives students an opportunity to work with volumes of cylinders, spheres and cones. Notice that the insight required increases as you move across the three glasses, from a simple application of the formula for the volume of a cylinder, to a situation requiring decomposition of the volume into two pieces, to one where a height must be calculated using the Pythagorean theorem.

Get independent practice working with the volumes of pyramids and Cones. Each incorrect response gets a text box explanation and another try. Correct responses are confirmed.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students discover the formula for finding the volume of a pyramid and apply the formula to solve problems.Key ConceptsThe volume of a pyramid is one-third the volume of a prism with the same base and height. The shape of the base does not matter (including if it’s a circle), and students will see the same one-third comparison between a cylinder and cone.GoalsUnderstand the formula for the volume of a pyramid.Apply the volume formula to solve problems.

This lesson describes the function and components of the human nervous system. It helps students understand the purpose of our brain, spinal cord, nerves and the five senses. How the nervous system is affected during spaceflight is also discussed in this lesson.

This collection includes 16 Peg + Cat video clips about geometry including 2-D and 3-D shapes.

Describes the important structures of the human eye and how they work so that we can see images. [4:47]

This video tutorial teaches you how to calculate the surface area and volume of cones. Just like pyramids and cylinders, there are formulas for surface area and volume of cones. Also included are questions on composite solids that consist of cones too. Step-by-step explanations are provided along with examples. [3:38]

In this virtual field trip find out about how volcanoes are formed and what kind of destruction can they cause. Discover how volcanoes affect our environment and where can you find active volcanoes on earth and on other planets.

This site from MathWorld describes characteristics of cones, names of various special cones, equations for a cone and many other equations relative to a cone. [Requires Java.]