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A solid cone has a lateral surface area of $100\pi$ square centimeters and a total surface area of $269\pi$ square centimeters. Find the base radius of the cone.

I would need to find the radius or height to solve this, but all it gives me is the lateral surface area of $100\pi$ and the total surface area of $269\pi$.

Both formulas require the height and the radius and it doesn't give me either. It wants me to find the base radius of the cone, the formula for that is $AB=\pi r^2$. I tried putting $269\pi$ (the number of the total surface area) in the formula: $269\pi= πr^2$, Which is $844.66= 3.14 r^2$ which would mean the radius is $9.9$. I tried putting in with the two formulas for the lateral surface area and total surface area, but they both don't work right with that number.

AnnieFireLovly
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    Using the information supplied, can you calculate the area of the circular base? – André Nicolas Aug 31 '15 at 19:25
  • More seriously: Just copying a question from homework (or wherever) has a fairly good chance of generating nothing but a few wisecracks and a reminder to add context in the form of how you've tried to solve the problem. A little effort goes a long way. – Brian Tung Aug 31 '15 at 19:49
  • I'm not asking for the answer but more of the formula to solve it. I cant figure out the radius or height of the surface area because the formula for surface area is A=πr(r+h2+r2), i dont have the height or radius, all i have is π. I can't figure out the lateral surface area either because the formula for that is AL=πr h2+r2, and again i dont have the height or radius, if i had one of them, like if i had the height, i could figure it out, but i dont have either. I tried putting random numbers in to match it, but no luck. – AnnieFireLovly Aug 31 '15 at 20:06
  • This is good, adding context of why you're having difficulty, and is exactly the type of stuff you should put in the question. I understand where you are having trouble now.

    Yes, it is true we don't know $r$ or $h$ yet, but we do know $A_s$ and $A_L$, so substitute those into your equations, and see if you can, using both equations, rearrange for $h$ in terms of $r$. You should then equate the two $h$s and see if you can get a value for $r$...

     – nathan.j.mcdougall Aug 31 '15 at 20:11
  • Did you forget a square root for $A_L?$ – Narasimham Aug 31 '15 at 20:28
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    Okay guys, with some rethinking I believe that the base radius of the cone is 13 centimeters. Thanks for all the help! – AnnieFireLovly Aug 31 '15 at 21:34
  • @AnnieFireLovly, That's right, well done – nathan.j.mcdougall Sep 01 '15 at 03:48

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