Question

Question partpointssubmissions usedthe base of a circular fence with radius 10 m is given by x = 10 cos(t), y = 10 sin(t). the height of the fence at position (x, y) is given by the function h(x, y) = 3 + 0.03(x2 − y2), so the height varies from 0 m to 6 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. (round your answer to two decimal places.)

Answer 1

If you unroll the fence, you find it has a length equal to the circumference of a circle of radius 10 m and an average height of 3 m. Its two-sided area will be

... A = 2·(3 m)·(2π·(10 m)) = 120π m²

Then the amount of paint required is

... (120π m²) × (1L)/(100 m²) = 1.2π L ≈ 3.77 L