Answer:
6.28 L
Step-by-step explanation:
The length of the circular fence is ...
C = 2πr = 2π(10 m) = 20π m
The height in terms of t is ...
h(t) = 5 +0.05((10cos(t))^2 -(10sin(t))^2) = 5 +5(1 -2sin(t)^2)
For 0 ≤ t ≤ 2π, the average value of this height function is 5.
The fence has an average height of 5 m and a length of 20π m, so an area of ...
(one side) fence area = (5 m)(20π m) = 100π m²
The area of both sides is double this, or ...
total fence area = 2(100π m²) = 2π(100 m²)
Since 1 liter covers 100 m², we need 2π liters to cover the fence.
The amount of paint needed is 6.28 L.
