An triangular prism is being filled with water at a constant rate of 0.5m^3 per minute. the Prism is 6.0m long and the Isosceles triangle has a height of 2m with a base length of 3m.
sketch a graph, qualitatively, of the height of the water in the pool against time. Explain why the graph has a shape you have just sketched
sketch a graph, qualitatively, of the height of the water in the pool against time. Explain why the graph has a shape you have just sketched
-
Describe the relationship between the height and the base of the triangle
When h = 2, b = 3
When h = 0, b = 0
h = (2/3) * b
b = (3/2) * h
What's the formula for the volume of a prism?
V = B * l
B = area of base
l = length of prism
Now I'm going to imagine that this prism is inverted (the triangular portion is pointing downward), and I'm going to imagine this because it's easier for me to envision it
l = 6
h = h
b = (3/2) * h
V = 0.5 * t
t = number of minutes that have passed
V = (1/2) * b * h * l
0.5 * t = 0.5 * (3/2) * h * h * 6
t = 9 * h^2
Solve for h and now height is a function of time
t / 9 = h^2
h = sqrt(t / 9)
h = (1/3) * sqrt(t)
When h = 2, b = 3
When h = 0, b = 0
h = (2/3) * b
b = (3/2) * h
What's the formula for the volume of a prism?
V = B * l
B = area of base
l = length of prism
Now I'm going to imagine that this prism is inverted (the triangular portion is pointing downward), and I'm going to imagine this because it's easier for me to envision it
l = 6
h = h
b = (3/2) * h
V = 0.5 * t
t = number of minutes that have passed
V = (1/2) * b * h * l
0.5 * t = 0.5 * (3/2) * h * h * 6
t = 9 * h^2
Solve for h and now height is a function of time
t / 9 = h^2
h = sqrt(t / 9)
h = (1/3) * sqrt(t)