Difference between revisions of "Volume of a Sphere"
Kayla Murray (talk | contribs) (Created page with "Let's say that we want to find the volume of a sphere of radius <math>r</math> using volumes of revolution.") |
Kayla Murray (talk | contribs) |
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Let's say that we want to find the volume of a sphere of radius <math>r</math> using volumes of revolution. | Let's say that we want to find the volume of a sphere of radius <math>r</math> using volumes of revolution. | ||
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| + | We know that the equation of a circle of radius <math>r</math> centered at the origin is | ||
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| + | ::<math>x^2+y^2=r^2.</math> | ||
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| + | The upper half semicircle is given by: <math>y=\sqrt{r^2-x^2}.</math> | ||
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| + | (insert picture of semicircle) | ||
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| + | Now, we want to rotate the upper half semicircle around the <math>x</math>-axis. This will give us a sphere of radius <math>r.</math> | ||
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| + | (insert pictures) | ||
Revision as of 08:58, 27 August 2017
Let's say that we want to find the volume of a sphere of radius using volumes of revolution.
We know that the equation of a circle of radius centered at the origin is
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2+y^2=r^2.}
The upper half semicircle is given by: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=\sqrt{r^2-x^2}.}
(insert picture of semicircle)
Now, we want to rotate the upper half semicircle around the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} -axis. This will give us a sphere of radius Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r.}
(insert pictures)