MHB How Can I Visualize the Intersection of a Cone and a Sphere?

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To visualize the intersection of the cone defined by z = √(x² + y²) and the sphere x² + y² + z² = 2, cylindrical coordinates can be employed for integration. Users are seeking effective software solutions to graph both shapes simultaneously and highlight the intersecting volume. While hand-drawn sketches are possible, they often lack precision and clarity. Recommendations for software tools that can accurately render these 3D shapes and their intersection are encouraged. Effective visualization aids in understanding the volume being calculated.
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Find the volume of the solid that is enclosed by the cone $z=\sqrt{x^2+y^2}$ and the sphere $x^2+y^2+z^2=2$.

The integral is not difficult to set up using cylindrical coordinates, but I'm trying to get a better visualization of the volume I'm actually integrating. I can't seem to get Wolfram Alpha to graph both regions at the same time. Is there any way I can do that, or even better, have it to shade in that region?

(I have been able to graph it by hand, but it is a terrible sketch :( )
 
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Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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