# What is the circumference of the circle if the cylinder has 39 volume and height is 4?

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Given the cylinder whose volume is 39 and the height is 4. We need to find the circumference of the base of the cylinder.

We know that the volume of the cylinder is given by:

V = r^2*pi * h where v is the volume, r is the radius, and h is the height.

The, we will substitute with the given values.

==> 39 = r^2*pi* 4

==> r^2 = 39/4pi = 3.1 ( approx.)

==> r = 1.76 ( approx.)

Then we will calculate the circumference.

==> We know that the circumference formula is given by:

C = 2*pi *r

==> C = 2*pi * 1.76 = 11.07 ( approx.)

**Then, the circumference of the base of the cylinder is 11.07 units.**

We have to find the circumference of the circle if the cylinder has 39 volume and height is 4.

The volume of the cylinder is equal to the product of the area of the base and the height.

Let the radius of the base be r. The area is equal to pi*r^2.

Now pi*r^2*4 = 39.

r^2 = 39/4*pi

r = sqrt (39 / 4*pi)

Therefore the circumference of the circle is 2*pi*r

=> 2*pi*sqrt (39 / 4*pi)

=> 11.068 squared units

The cylinder's volume v is given by :

v = pr^2*h, where r=radius of cylinder, h is the height of the cylinder.

Given v = 39 and h = 4.

So substituting in the formula, we get :

pir^2*4 = 39.

r^2 = 39/4pi

r = sqrt(39/4pi)

Therefore r = sqrt(39/4pi).

Therefore the circumference C = 2pir

Substitute the value of r = sqrt(39/4pi) in C = 2pir :

C = 2pi*sqrt(39/4pi) = 11.07 nearly.

The circumference of the base circle of the cylinder is:

2pi*r

The volume of the circle is:

V = Abase*height

Abase = pi*r^2

From enunciation we know the values of the vloume and the height:

39 = pi*r^2*4

We'll divide by 4pi and we'll get:

r^2 = 39/4pi

r = sqrt39*sqrtpi/2pi

The circumference is:

C = 2pi*(sqrt39*sqrtpi/2pi)

We'll simplify to:

**C = sqrt(39*pi) units**

**or**

**C = 11.0448 units**