1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Surface area of a cone

  1. Aug 22, 2015 #1

    DGK

    User Avatar

    1. The problem statement, all variables and given/known data

    Determine a simplified, factorised expression, in terms of the radius (r), for the surface area of a cone where diameter (D) = perpendicular height (h)

    2. Relevant equations

    A = πr (r + √(h^2 + r^2))

    3. The attempt at a solution

    h=D=2r

    A = πr (r + √(2r^2 + r^2))

    A/π = r (r + √(2r^2 + r^2))
     
    Last edited: Aug 22, 2015
  2. jcsd
  3. Aug 22, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You can factorise the inside of your square root, which will set the scene for further simplification. Ideally you want to get r outside of the square root.
     
  4. Aug 22, 2015 #3

    DGK

    User Avatar

    A/pi = r (r + sqrt( r (2r + r))


    Is this right? I really don't know what I'm doing!!
     
  5. Aug 22, 2015 #4

    DGK

    User Avatar


    Thanks for your response!!

    See above for my reply....sorry I'm new to this!!
     
    Last edited: Aug 22, 2015
  6. Aug 22, 2015 #5

    Nathanael

    User Avatar
    Homework Helper

    You could've factored out another r from the red part. Then use ##\sqrt{a^2b}=\sqrt{a^2}\sqrt{b}=a\sqrt{b}##.

    Also no need to divide both sides by pi, you want to find A not A/pi.

    And what is h2? You seem to say its 2r2.
     
  7. Aug 22, 2015 #6

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    DGK there's a further problem that the formula you give for A in the OP under '2. Relevant Equations' is wrong. Show the working by which you got to that formula, and somebody will show you where you went wrong.
     
  8. Aug 23, 2015 #7

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You miss the parentheses around 2r.
     
  9. Aug 23, 2015 #8

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The relevant equation A = πr (r + √(h^2 + r^2)) is correct.
     
  10. Aug 23, 2015 #9

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is if you include the base. I assumed he wasn't.
     
  11. Aug 23, 2015 #10

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Why? It would be the lateral surface area.
     
  12. Aug 23, 2015 #11

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Here's another way of looking at it. A cone with base radius r and height h has "slant height" [itex]\sqrt{r^2+ h^2}[/itex] by the Pythagorean theorem. Imagine cutting a slit from the base to the tip of the cone, then flattening it. (A cone is a "developable surface" and can be flattened without warping.)

    It will flatten to part of a disk with radius [itex]\sqrt{r^2+ h^2}[/itex]. To see what part, look at the two circumferences. Since the cone had base radius r, the circumference of that base is [itex]2\pi r[/itex]. A circle with radius [itex]\sqrt{r^2+ h^2}[/itex] has circumference [itex]2\pi\sqrt{r^2+ h^2}[/itex].

    [ mod edit ]
     
    Last edited by a moderator: Aug 23, 2015
  13. Aug 25, 2015 #12
    Isn't the relevant equation
    πr^2 + πrL
    L = √(r^2+h^2)
    = √(r^2+(2r)^2)
    L^2 = r^2+(2r)^2
    = (3r)^2
    L = √3r
     
  14. Aug 25, 2015 #13

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is wrong. Expand (2r)^2. It is not 2r^2!
     
  15. Aug 25, 2015 #14
    Then:
    TSA = πr^2 + πr√3r
    = πr^2 + √3πr^2
    = πr^2(1+√3)
     
  16. Aug 25, 2015 #15
    Ahhh ok thanks heaps (this exact question is in my assignment)
    would it instead be:
    L^2 = r^2 + (2r)^2
    = r^2 + 4r^2
    = 5r^2
    L = √5r
    or
    L = 5√r
    ?
     
  17. Aug 25, 2015 #16

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Which one do you think? How do you apply the square root to a product? What is √(ab)?
     
  18. Aug 25, 2015 #17
    so is it:
    L = √5r
    or
    L = 5√r
     
  19. Aug 25, 2015 #18

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You have to know. Answer my question: √(ab)=???
     
  20. Aug 25, 2015 #19
    The next part of the question is:
    A rectangular prism has:
    - Height equivalent to the slant height (L) of the cone in part a
    - Length twice the diameter of the cone in part a
    - width 5 times the radius of the cone in part a
    Determine a simplified factorised expression, in terms of the radius (r), for the volume of the rectangular prism.

    All i have so far is:
    V = LxWxH
    H = √5r or 5√r
    L = 2D = 2(2r) = 4r
    W = 5r
    V = 4r x 5r x ...
    and I don't know where to go from there.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Surface area of a cone
  1. Surface Area help (Replies: 3)

Loading...