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.
To find the volume of water in the trough, we can use the formula for the volume of a trough-shaped object, which is given by:
V = (1/2) * L * W * D
Where:
V is the volume
L is the length
W is the width
D is the depth
Given information:
L = 10 meters
W = 4 meters
D = 2 meters
Substituting these values into the formula, we get:
V = (1/2) * 10 * 4 * 2
Simplifying the expression, we get:
V = 20 * 4
V = 80 cubic meters
Therefore, the volume of water in the trough is 80 cubic meters.
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