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.)

Question

Mathematics

Paxton

10 January, 23:53

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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Louisa · 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.