Factoring of polynomials [Please help :(]

[Vempy]

Word problems are the bane of my existence.

A fuel tank is in the shape of a horizontal right circular cylinder with a hemisphere on each end. If the length of the cylinder is 10 m, and the volume is 2000m^3. find the common radius of the hemispheres and the cylinder.

Volume of a cylinder= πr^2h
Volume of a sphere= 4/3πr^3

Therefore,
Volume of the tank= 4/3πr^3 + πr^2h

2000=4/3πr^3 + 10πr^2
0=4/3πr^3 + 10πr^2 - 2000

Now, to solve for the value of r I have to factor the polynomial. To do that I need to find the factor for the trinomial then using that long divide and find the quadratic that corresponds with that factor. From there I need to factor or use the quadratic roots formula.

However, I'm not sure how to get past the point of the general equation.

How would you find a factor for 0=4/3πr^3 + 10πr^2 - 2000 when there are the π's to consider?



(π = pi, incase anyone wasn't sure. It doesn't look much like pi to me either.)

 

[galactus]

This cubic has one real solution and two complex. Of course, you need the real one.

There are different ways, but are you familiar with Newton's method(assuming you've had calculus)?.

A couple of iterations gives you the answer.

Also, you could use the Intermediate Value theorem, per se, and get close

For instance, use r=5.9 in your equation. That gives 1953.877

r=6 gives 2035.752

The solution must be between 5.9 and 6. Whittle it down.

 

[Vempy]

I'm in high school Calculus, grade 12 course, and it's the very beginning of the semester still so I haven't heard of Newton's method. What it should be based on is the factor theorem.