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Ice-Cream Cone problem - Volume in Spherical Coord

  1. Nov 24, 2015 #1
    1. The problem statement, all variables and given/known data
    S is the sphere of equation x2 + y2 + z2 = 10z and C the cone of equation
    z= sqrt(3*( x2 + y2)) . The axes are measured
    centimeters.
    R of sphere = 5
    D = 10

    Total height is 10 cm

    Illustrate the solid E bounded by the C cone and the sphere S and calculate its volume using the details
    Spherical.

    2. Relevant equations


    3. The attempt at a solution
    To find phi:
    x=0
    z= sqrt(3*( x2 + y2))
    z= sqrt(3*( 02 + y2))
    z= y*sqrt(3)

    y= 3 <== I picked 3, could of picked any number, its just to find the Z and then find the angle.
    z= 3*sqrt(3)

    tan(phi)=3/(3*sqrt(3))
    phi = pi/6 ===30degree

    Theta = 2*pi

    $=integral
    2*pi$0 pi/6$0 10*cos(phi)$0 p2*sin(phi) dp dphi dtheta

    229.074cm3
     
  2. jcsd
  3. Nov 24, 2015 #2

    LCKurtz

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    I didn't check the value of your integral but it looks like it is set up correctly. Why give a decimal instead of exact answer?
     
  4. Nov 24, 2015 #3
    I am used to give decimal as my teacher always ask for that.
     
  5. Nov 25, 2015 #4

    LCKurtz

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    Nevertheless, what you should routinely do is give the exact answer if it is practical, and at the very end put the decimal approximation. For example, if the exact answer is ##\frac {\sqrt 3} 5## you could write it like this:
    $$\text{Your Variable }=\frac {\sqrt 3} 5 \approx .3464$$That would be correct, good form, and would satisfy your teacher.
     
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