Ice-Cream Cone problem - Volume in Spherical Coord

1. Nov 24, 2015

masterchiefo

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. Nov 24, 2015

LCKurtz

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?

3. Nov 24, 2015

masterchiefo

I am used to give decimal as my teacher always ask for that.

4. Nov 25, 2015

LCKurtz

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.