# Question #1be57

##### 1 Answer

The cylinder has radius,

#### Explanation:

If you put the center of the cone on the y axis and look at the cross-section of the cone in the x-y plane, it is a triangle that intersects the y axis at 4.5 and the x axis at 5.5; the equation of that line is:

We want to find the point where the cylinder intersects this line such that its volume is maximized:

But we are looking at these solid objects as cross-sections in the x-y plane so

Substitute the right side of equation [1] for y in equation [2]:

Compute the first derivative with respect to x:

Set the first derivative equal to zero:

Divide by

(Please notice that we got rid of the root x = 0 but that is clearly a minimum)

Solve for x:

Do the second derivative test:

It is clearly a maximum.

Substitute

Translating back to r and h:

The cylinder has radius,