2.9 Geometry

Properties of Circles

An image of a circle is shown. There is a line drawn through the widest part at the center of the circle with a red dot indicating the center of the circle. The line is labelled d. The two segments from the center of the circle to the outside of the circle are each labelled r.
Figure 2.3. Properties of a circle.
  • [latex]r[/latex] is the length of the radius
  • [latex]d[/latex] is the length of the diameter
  • [latex]d=2r[/latex]
  • Circumference is the perimeter of a circle. The formula for circumference is

    [latex]\begin{align*}C=\frac{2}{\pi r}\end{align*}[/latex]

  • The formula for area of a circle is

    [latex]A=\pi r^2[/latex]

Remember, that we approximate [latex]\pi[/latex] with [latex]3.14[/latex] or [latex]\frac{22}{7}[/latex] depending on whether the radius of the circle is given as a decimal or a fraction. If you use the [latex]\pi[/latex] key on your calculator to do the calculations in this chapter, your answers will be slightly different from the answers shown. That is because the [latex]\pi[/latex] key uses more than two decimal places.

Volume and Surface Area of a Sphere

For a sphere with radius [latex]r[/latex]:

An image of a sphere is shown. The radius is labelled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.
Figure 2.4. Volume and Surface Area of a Sphere.

Attribution

“9.5 Solve Geometry Applications: Circles and Irregular Figures” and “9.6 Solve Geometry Applications: Volume and Surface Area” from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax are licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

License

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Fanshawe College Astronomy Copyright © 2023 by Dr. Iftekhar Haque is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.