# How do you find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2?

The answer is:

We can imagine a vertical section of the figure, that would appear:

Let

Let's put

In the right-angled triangle

So the volume of the cone is:

Now let's find the signum of the derivative, since

So:

The first one has only the solution:

the second:

The function growths from zero to

So

Let's find now

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To find the dimensions (radius r and height h) of the cone of maximum volume inscribed in a sphere of radius 2, the radius and height of the cone can be related using similar triangles. The volume of the cone can then be expressed in terms of one variable, which can be maximized using calculus. The resulting dimensions are ( r = \frac{4}{3}\sqrt{2} ) and ( h = \frac{8}{3} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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