Final answer:
To find the volume of the cylinder, calculate the radius first using the equation for surface area. Then, use the formula V = πr²h to determine the volume. Finally, find the circumference of the base using C = 2πr.
Step-by-step explanation:
To find the volume of the cylinder, we can use the formula V = πr²h, where r is the radius of the base and h is the height. However, we need to find the radius before we can calculate the volume. We know that the total surface area of the cylinder is 6512 cm². The formula for the surface area of a cylinder is A = 2πrh + πr², where r is the radius and h is the height. Given the surface area, we can solve for r using this equation.
6512 = 2πrh + πr²
Next, we can use the value of r to calculate the volume of the cylinder using the formula V = πr²h.
Once we have calculated the volume, we can determine the circumference of the base of the cylinder using the formula C = 2πr.
So, the answer is D. 1728 cm³.