Volume of a cone using spherical coordinates with integration

[mahrap]

Find the volume of a cone with radius R and height H using spherical coordinates.


so x^2 + y^2 = z^2
x = p cos theta sin phi
y= p sin theta sin phi
z= p cos phi

I found theta to be between 0 and 2 pie
and phi to be between 0 and pie / 4.
i don't know how to find p though. how would i do this.

 

[haruspex]

so x^2 + y^2 = z^2

That does not fit the given dimensions.

x = p cos theta sin phi
y= p sin theta sin phi
z= p cos phi

I found theta to be between 0 and 2 pie
and phi to be between 0 and pie / 4.
i don't know how to find p though. how would i do this.

After correcting the equation for the cone, consider the coordinates of a point at the circumference at the widest part of the cone.