# Calculate the height of the cylinder if the volume is 42 and the circumference of the base is 6pi.

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The volume of a cylinder is given by the product of the area of the base and the height.

Here we have volume given as 42 and the circumference of the base is 6*pi.

The circumferance is 2*r*pi = 6*pi

=> r = 3

The area of the base is pi*r^2 = 9*pi

9*pi*height = 42

So the height is 42/ (9*pi)

=> height = (14/3)/ pi

**The required height is (14/3)/pi.**

Given that the volume of a cylinder is 42

Then we will write the formula of the cylinder:

V = r^2 * pi * h = 42 where r is the radius and h is the height.

Then, we need to determine the radius using the circumference of the base.

We know that the circumference is given by:

C = 2* r * pi = 6pi

==> r = 6pi/ 2pi = 3

==> r= 3

Now we will substitute into the volume.

==> r^2 * pi * h = 42

==> 9 * pi * h = 42

==> h= 42/9pi = 14/3pi = 1.49 ( approx.)

**Then, the height of the cylinder is 14/3pi = 1.49 units. **

The formula relating to the circumference C and volume v of the cylinder are C = 2pi*r and v = pr^2*h, where r is the radius and h is the height of the cylinder.

By data C = 6pi and v = 42.

=> 2pir = 6pi, So r = 6pi/2pi = 3.

So the radius r = 3.

Also given v = 42 => pi*r^2 h= 42

=> h =42/pi2^2 = 42/pi*3^2 = 42/9pi = 1.4854 units.

So the height of the cylinder is 1.4854 units.