Question

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.)

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.