Answer:
I believe the answer is 1.36666666667

Step-by-step explanation:
Since one of the boundaries is y = 0, we need to find the roots of the function
. Using the quadratic equation, we get

But since the region is also bounded by
, that means that our limits of integration are from
(instead of -3) to
.
Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by





X = short section of rope
4x = longer section of rope
x + 4x = 25
5x = 25
x = 5
…or in other words the shorter piece of rope is 5 feet long
40 - 10 - 14 = 16
so my answer is 16