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# Spheres

## Volume and surface area of 3D circles.

Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.
• Read

## Spheres

by CK-12 //at grade

This concept teaches students how to calculate the volume and surface area of a sphere.

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• PLIX

## Spheres: Surface Area of a Sports Ball

by CK-12 //at grade

Spheres Interactive

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• Video

## Spheres Principles

by CK-12 //at grade

This video gives more detail about the mathematical principles presented in Spheres.

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• Video

## Spheres Examples

by CK-12 //at grade

This video shows how to work step-by-step through one or more of the examples in Spheres.

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• Practice
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## Spheres Practice

by CK-12 //at grade
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• Critical Thinking

## Spheres Discussion Questions

by CK-12 //at grade

A list of student-submitted discussion questions for Spheres.

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• Post Read

## Spheres Post Read

by CK-12 //at grade

To stress understanding of a concept by summarizing the main idea and applying that understanding to create visual aids and generate questions and comments using a Concept Matrix.

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• Pre Read

## Spheres Pre Read

by CK-12 //at grade

To reinforce and increase concept comprehension, and to analyze similarities and differences between topics using a Two Column Table.

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• Post Read

## Spheres Four Square Concept Matrix

by CK-12 //at grade

Summarize the main idea of a reading, create visual aids, and come up with new questions using a Four Square Concept Matrix.

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• Real World Application

## Where We Live!

by CK-12 //at grade

Discover the geometry of the shape of the Earth.

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• Study Guide

## Spheres Study Guide

by CK-12 //at grade

This study guide looks at the characteristics of spheres, surface area, and volume of spheres.

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• Link

## Derivation of the Formula for the Surface Area of a Sphere

by CK-12 //at grade

The surface area of a sphere is opened up to illustrate how the formula for the surface area of a sphere can be understood.

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• Link

## Derivation of the Volume of a Sphere

by CK-12 //at grade

The volume of a sphere is mapped into an equivalent pyramid to illustrate how the formula for the volume of a sphere can be understood.

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