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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
If the surface area of the base is also included it is 168*pi + 2*pi*49
=> 168*pi + 98*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.
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