consider the parabola y = ax^2
with (2,3) on the graph. Then a = 3/4
y = 3/4 x^2
x = 2/√3 √y
The cross-section area of the water is
a = 2∫[0,2] x dy = 2∫[0,2] 2/√3 √y dy = 16/9 √6 m^2
So the volume of water is 16/9 √6 * 10 = 160/9 √6 m^3
A parabolic trough 10 meters long, 4 meters wide across the top and 3 meters deep is filled with water at a depth of 2 meters. Find the volume of water in the trough.
1 answer
1 answer