CIRCLES AND SPHERES

By: Mikolaj Pal - Cousino High School

Sebastien Rivest - South Lake High School

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Common Core State Standards

The CCSS requires that all 7th Graders know: The formulas for the area and

circumference of a circle. The relationships between the

circumference and the area of a circle.

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Center of a Circle or Sphere

The center of a circle or sphere is the point in the very center of the circle. The radius will always be the same if the midpoint is correct.

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Circumference

The circumference of a circle is the distance around the circle. Usually the letter C is used for it in equations.

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Radius

The radius is the distance from the center of the circle to the circumference. As long as the midpoint is correct, the radius will never change.

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A Radius Always Remains the Same

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Diameter

The diameter is the distance from one side of a circle to the other side through the center. The diameter is twice the distance of the radius.

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Pi

Pi (π) is a number (approx. 3.14) that is the circumference of any circle divided byits diameter.

Pi to ten places:3.141592653589793238462

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Chord

A chord is a line segment connecting a point of the circle to another in a circle. IT IS NOT A DIAMETER because it doesn’t pass through the center.

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Secant

A secant is a line that connects two points of a circle like a chord, but it’s also a line that passes through the circle.

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Tangent

A tangent is a line that is perpendicular to the radius or diameter that just “touches” the edge of the circle.

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Developing the Formula for a Circumference

The formula for a circumference can be developed in two ways. With D=diameter, the equation is C=πD. With R=radius, the equation is C=π(R*2).

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Example of Finding the Circumference

Diameter = 8cm.

π * 8cm.= 25.1327cm.2

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Area of a Circle

The area of a circle is the space inside of the circumference. The common equation for the area of a circle is A=πr^2. Using the circumference it is A=C^2/4π, and with a diameter it is A=(π/4) * D^2.

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Example of Finding the Area of a Circle

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The Formulas Also Work Backwards

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Real Life Applications

Circles are used in many places in real life including CD’s, Tires, and clocks. For these products to properly function, the manufacturer(s) must properly produce it to meet the diameter and circumference specifications that are required.

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Conclusion

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Any Questions?

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Let’s See What You Know

Diameter=12cm.Circumferenc

e:Area:

Radius=6cm.

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Sources

http://www-history.mcs.st-and.ac.uk/HistTopics/1000_places.html

http://www.mathsisfun.com/geometry/circle-area.html

http://www.aaamath.com/geo612x4.htm