1. ## Cylinder Problem

I have a maths question that I can't solve. It reads as follows:

"A small cylinder is placed on the top of two identical cylinders, which are touching each other as shown in the diagram. Find the radius of the small cylinder."

The diagram can be seen here:

2. ## Re: Cylinder Problem

Originally Posted by hholbrook
I have a maths question that I can't solve. It reads as follows:

"A small cylinder is placed on the top of two identical cylinders, which are touching each other as shown in the diagram. Find the radius of the small cylinder."

The diagram can be seen here:

1. I've modified your sketch a little bit (see attachment)

2. The radius of one of the bigger pipes is R = 3, the radius of the smaller pipe is r. h and the 2 radii form a right triangle:

$\displaystyle h^2 = (3+r)^2-3^2 = r(6+r)~\implies~h=\sqrt{r(6+r)}$

3. The total height of the bundle of pipes is 9:

$\displaystyle 9 = r+h+3 = r+\sqrt{r(6+r)}+3$

4. Solve for r.
Spoiler:
You should come out with r = 2