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A length 550cm3 of thin thread was wrapped around a cylinder 25 times.Calculate the circumference and radius of the cylinder

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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.

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