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

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The volume of a cylinder with the radius of the base equal to r and the height equal to h is given by is given by pi*r^2*h. The surface area is 2*pi*r*h

Here we have the volume as 588*pi and the height as 12

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

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

=> r^2 = 49

=> r = sqrt 49

=> r = 7

The surface area of the curved surface is 2*pi*r*h = 2*pi*7*12

=> 168*pi

If the surface area of the base is also included it is 168*pi + 2*pi*49

=> 168*pi + 98*pi

=> 266*pi

**The required total surface area of the cylinder is 266*pi**

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.**