Find the surface area of the cylinder if the volume = 588*pi and the height is 12.

We will determine the radius using the volume
formula.

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

==> 588pi = r^2 * pi *
12

We will reduce
pi.

==> 588 = r^2 *
12

Now we will divide by
12.

==> r^2 = 588/12 =
49

==> r = 7

Now let us
calculate the surface area.

==> surface area =
2*area of the base + area of the sides.

==> area of
the base = r^2 * pi= 7^2*pi = 49pi

area of the side =
circumference * h = 2*pi*r *h = 2*7*pi*12 =
168pi.

==> surface area = 2* 49pi + 168pi= 98pi +
168pi = 266pi = 835.66

Then the
surface area of the cylinder is SA = 266pi = 835.66 square
units.