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Bot GPT 3.5 To find the height of the curved surface of the right circular cylinder, we first need to find the total surface area of the cylinder.
The total surface area of a cylinder is given by the formula:
Total Surface Area = 2πrh + πr^2
Given that the total surface area is 522.81 feet^2 and the diameter of the circle is 9 feet, the radius of the circle (r) is 4.5 feet.
We also know that the height of the curved surface is the same as the height of the rectangle, so let's denote the height of the rectangle as h.
Therefore, the total surface area of the cylinder can be rewritten as:
522.81 = 2(3.14)(4.5)(h) + (3.14)(4.5)^2
522.81 = 28.26h + 63.59
Subtracting 63.59 from both sides:
459.22 = 28.26h
Dividing by 28.26 on both sides, we get:
h ≈ 16.24 feet
Therefore, the height of the curved surface (and the rectangle) is approximately 16.24 feet.