Answer:
We can use the given information to solve for the circumference and radius of the cylinder.
Let's start by finding the total length of the thread:
total length = length of thread per wrap * number of wraps
In this case, the length of thread per wrap is the circumference of the cylinder. So, we can write:
total length = circumference * 25
We also know that the volume (V) of the cylinder is 550 cm³. We can use the formula for the volume of a cylinder:
V = πr²h
Since the cylinder has been wrapped 25 times by the thread, its height is the length of the thread per wrap. So, we can write:
V = πr² * circumference
550 = πr² * circumference
We have two equations for circumference: one from the total length of the thread and one from the volume of the cylinder. We can set them equal to each other:
circumference * 25 = 550 / r²π
circumference = 22 / r²
Substituting this expression for circumference into our volume equation, we have:
550 = πr² * (22 / r²)
Simplifying:
550 = 22π
r = sqrt(25 / pi) cm
Now that we have the value of the radius, we can use the equation for circumference to find its value:
circumference = 2πr = 10π cm
Therefore, the circumference of the cylinder is 10π cm and its radius is sqrt(25 / pi) cm.