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

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.