A cylindrical pipe is 25 ft long and has a volume of 900ft3 find it's approximate diameter to the nearest hundredth of a foot
1 answer:
Answer:
Diameter of the pipe ≈ 6.77 ft
Step-by-step explanation:
Volume of a cylinder = πr²h
Here, r = Radius of the cylindrical pipe
h = Length of the pipe
Volume of the pipe = 900 ft³
Length of the pipe = 25 ft
By substituting the given values in the formula,
900 = π(r)²(25)
r² =
r = √11.459
r = 3.385
Diameter = 2(radius)
= 2(3.385)
= 6.77 ft
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Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.