Question: Please show every step and use calculus notation please. I am getting a different answer and can't figure out what I'm doing wrong or leaving

Please show every step and use calculus notation please. I am getting a different answer and can't figure out what I'm doing wrong or leaving out. Thank you!

3. A line segment of length 2 has its center at the point (2, 5) and makes an angle of 6 with horizontal. What value of 6 will result in the largest surface area when the line segment is rotated about the yaxis? Explain your reasoning

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