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update guide-text for 'surface-area-of-a-cone' (#26002)

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update guide-text for 'surface-area-of-a-cone' with proper-text, expressions and video-link
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Pritom Gogoi
2018-10-23 14:07:28 +05:30
committed by Randell Dawson
parent 045ddc156c
commit 49eb6e7408
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guide/english/mathematics/surface-area-of-a-cone/index.md
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@ -3,13 +3,28 @@ title: Surface Area of a Cone
---
## Surface Area of a Cone
This is a stub. <a href='https://github.com/freecodecamp/guides/tree/master/src/pages/mathematics/surface-area-of-a-cone/index.md' target='_blank' rel='nofollow'>Help our community expand it</a>.
A cone is a three-dimensional solid that has a circular base, which is connected by a curved surface to its vertex. The curved surface of the cone is formed by a set of line segments that connect the vertex to the circumference of the circle at the bottom.
<a href='https://github.com/freecodecamp/guides/blob/master/README.md' target='_blank' rel='nofollow'>This quick style guide will help ensure your pull request gets accepted</a>.
The `radius of the cone 'r'` is defined by the radius of the circle formed at the bottom. The `slant height 'l'` is the distance from any point on the circle to the vertex of the cone. Lastly, `the altitude 'h'` is defined by the distance measured from the vertex to the cirle's center.
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
* The `slant height 'h'` is calculated as:
<a href="http://www.codecogs.com/eqnedit.php?latex=l&space;=&space;\sqrt{r^2&plus;a^2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?l&space;=&space;\sqrt{r^2&plus;a^2}" title="l = \sqrt{r^2+a^2}" /></a>
* The `lateral surface area` is given by: <a href="http://www.codecogs.com/eqnedit.php?latex=L&space;=&space;\pi&space;r&space;l&space;=&space;\pi&space;r&space;\sqrt{r^2&plus;h^2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?L&space;=&space;\pi&space;r&space;l&space;=&space;\pi&space;r&space;\sqrt{r^2&plus;h^2}" title="L = \pi r l = \pi r \sqrt{r^2+h^2}" /></a>
* The `base surface area` is given by: <a href="http://www.codecogs.com/eqnedit.php?latex=B&space;=&space;\pi&space;r^2" target="_blank"><img src="http://latex.codecogs.com/gif.latex?B&space;=&space;\pi&space;r^2" title="B = \pi r^2" /></a>
Hence, the total surface area of the cone is the sum of the `lateral surface area` and the `base surface area`.
<a href="http://www.codecogs.com/eqnedit.php?latex=A=&space;L&space;&plus;&space;B&space;=&space;\pi&space;r&space;l&space;&plus;&space;\pi&space;r^2&space;=&space;\pi&space;r&space;(l&space;&plus;&space;\pi&space;r)&space;=&space;\pi&space;r&space;(\sqrt{r^2&plus;h^2}&plus;&space;\pi&space;r)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?A=&space;L&space;&plus;&space;B&space;=&space;\pi&space;r&space;l&space;&plus;&space;\pi&space;r^2&space;=&space;\pi&space;r&space;(l&space;&plus;&space;\pi&space;r)&space;=&space;\pi&space;r&space;(\sqrt{r^2&plus;h^2}&plus;&space;\pi&space;r)" title="A= L + B = \pi r l + \pi r^2 = \pi r (l + \pi r) = \pi r (\sqrt{r^2+h^2}+ \pi r)" /></a>
<img src="https://qph.fs.quoracdn.net/main-qimg-7e85a657d49edce7ee0b914024017acf.webp">
#### More Information:
<!-- Please add any articles you think might be helpful to read before writing the article -->
* The derivation for the formula can be found at - [mathopenref.com](https://www.mathopenref.com/coneareaderivation.html)
* The link to a video explaining the derivation is given below:
<a href="http://www.youtube.com/watch?feature=player_embedded&v=rd8tbD2eekM
" target="_blank"><img style="display: block; margin: 0 auto" src="http://img.youtube.com/vi/rd8tbD2eekM/0.jpg"
alt="Video Thumbnail Image" width="400" border="2"/></a>