The base of a circular fence with radius 10 m is given by x = 10cos (t), y = 10sin (t). the height of the fence at position (x, y) is given by the function h (x, y) = 2 + 0.01 (x2 - y2), so the height varies from 1 m to 3 m. suppose that 1 l of paint covers 100 m2. determine how much paint you will need if you paint both sides of the fence. (give your answer correct to two decimal places.)

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Mathematics

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27 November, 04:00

The base of a circular fence with radius 10 m is given by x = 10cos (t), y = 10sin (t). the height of the fence at position (x, y) is given by the function h (x, y) = 2 + 0.01 (x2 - y2), so the height varies from 1 m to 3 m. suppose that 1 l of paint covers 100 m2. determine how much paint you will need if you paint both sides of the fence. (give your answer correct to two decimal places.)

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Jorden Hines · Answer 1

The average height of the fence is 2 m; its length is 20π m. So, its 2-sided area is

A = 2 * (2 m) * (20π m) = 80π m² ≈ 251 m²

At 1 L / (100 m²), it will take 2.51 L of paint to paint both sides.