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I've been struggling with this for so long and I never got a chance to ask my teacher how to solve it.

If the surface of the cone is $360\pi$ and $s = 26 \text{cm}$, calculate the volume of that cone.I found the solution but there is no explanation, somehow you need to get to squared binomial and I'm not sure why.

Formula for the cone volume: $V = \frac13\cdot\pi\cdot r^2\cdot H$

Formula for the cone surface: $P = \pi\cdot r\cdot(r+s)$

5xum
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user3711671
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  • What is the shape of your cup? and what is $s$? – Surb Jul 22 '14 at 08:47
  • You don't know what s is?But isn't math the same in every country?small s is this http://profesorka.files.wordpress.com/2013/06/slika321.gif (not the entire green triangle but the line on the right that goes from bottom to the top, s is actually the side of the cone, so everything except the base is actually s, except the height of course).Anyway there isn't any shape mentioned so i guess it's just a regular cone, keep in mind that this is from the 9th (and last) year of elementary school so we probably haven't done every shape of cones. – user3711671 Jul 22 '14 at 08:50
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    "You don't know what s is?But isn't math the same in every country?..." A cone is a cone in every country but the signification of $s$ may be different from one teacher to another or from one book to another... E.g. the wikipedia article about cone don't use $s$ in any dimension of the cone: http://en.wikipedia.org/wiki/Cone – Surb Jul 22 '14 at 08:56
  • Math is the same in every country but $s$ is not the same in every context. – Tunococ Jul 22 '14 at 08:57

2 Answers2

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First off, write the formula for the cone volume, and the formula for the cone surface. Edit your question with them, and I will edit my answer to help you further.

EDIT:

Using the formula for $P$, can you extract what $r$ is? (hint: yes you can) Then, once you have $r$, you can calculate $V=\frac13 \pi r^2 H$, as long as you can calculate $H$ from $r$ and $s$ (which you can, using a very famous theorem).

5xum
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$SA = \pi rs + \pi r^2$. Thus: $360\pi = \pi 26r + \pi r^2 \to r^2 + 26r = 360 \to (r+13)^2 = 23^2 \to r = 10$. Then $h = \sqrt{s^2 - r^2} = \sqrt{26^2 - 10^2} = 24$. We can now find $V$, and $V = \dfrac{\pi r^2h}{3} = \dfrac{\pi 10^2\cdot 24}{3} = 800\pi$

DeepSea
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  • Way to go, you solved the whole task for the OP. Don't you think he would learn more if he only recieved hints, so that he could solve it on his own? – 5xum Jul 22 '14 at 09:07
  • I found the same thing in solutions, but where did π disappear after the first arrow?By the way 5xum i tried to do it the same way you told me few months ago and I am asking this because of the 1st sentence in this comment. – user3711671 Jul 22 '14 at 09:15
  • But there are 2 pis on the right side and only 1 on the left, so shouldn't there still be 1 pi left? – user3711671 Jul 22 '14 at 09:18
  • @user3711671 if $\pi\cdot (a+b) = \pi\cdot c$, then $a+b = c$. – 5xum Jul 22 '14 at 09:20
  • Thanks, I can't believe how i missed that.This doesn't seem difficult if you have at least some basic math skills but it's interesting how this task is marked with the 'difficult' mark in our book. – user3711671 Jul 22 '14 at 09:41