University level math?

Question

Horrible question...Does it even have an answer?



A cone is circumscribe around a sphere. The radius of the sphere is 5 units.

The accompanying illustration is of an equilateral triangle (although you cannot assume that this is correct) with a circle touching all three sides, almost like a tangent. From the bottom left corner to the circle’s center there is a line, where the radius is shown as 5 and the rest of the way to the corner is x. From the centre of the circle, strait down the bottom of the original triangle forms a line of 5 units and a 90 degree angle. All of this forms a second triangle inside the first. We were told this is so the you can use the Pythagorean Theorem.

a) Write a formula for the volume, V, of the cone in terms of x. What kind of function is V?
b) Determine the roots of the function in part a. Do the roots have any geometrical meaning? Explain.
c) What is the domain of the function in part

Find picture here:

http://www.flickr.com/photos/14562815@N06/1481705611/

Actual diagram...

http://www.flickr.com/photos/14562815@N06/1484006615/

Obviously I'm just as bad with computers as I am at math...

Answer 1

I would love to attempt this question, but I'm getting a headache trying to figure out what the diagram looks like. It would really help if you uploaded the diagram on a website, then added a link using the "add details" feature.

I can't see the figure, it says it has been deleted.
But if you have a cone circumscribing a sphere, let's consider the plane through both their centers. It would look like a triangle circumscribing a circle.

Let's call the triangle ABC, where A is the apex of the cone. BC would be the diameter of the top of the cone.
Let O be the center of the sphere.
Let θ = angle OAC = angle OAB
Let D be the midpoint of BC
ie DC = DB = R, OD = r

OA = r*cscθ
h = r*cscθ + r = r*(cscθ+1)
DC = R = h*tanθ
V = π/3 R^2 h
= πh^3*tan^2 θ / 3
= πr^3/3 * tan^2 θ *(cscθ+1)^3

From your description, it sounds like
OA = x+r
cscθ = (x+r)/r
tan^2 θ = r^2 / [x*(x+2r)]

V = πr^2 / 3 * (x+2r)^2 / x

There are no roots of this equation, neither can there be, because there is no way the cone circumscribing the sphere can have zero volume.
The domain is x > 0

Answer 2

You change your question and Dr D changed his answer

I do not know why I even answer these questions!