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Related rates q (1 Viewer)
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ExtremelyBoredUser
Bored Uni Student
Always draw a diagram to make the question easier, thats the trick with related rates. Make sure you know the respective formulas for all types of shapes; cones, spheres, pyramids.
dV/dt = 20 cm^3/s
Given parameters:
dV/dt = 20, find dh/dt, area and surface area.
V = pir^2 h^3/3
h = r as the angle is 45 degrees so tan45=1
Therefore
V = pi*h^3/3
dV/dh = pi * h^2
dh/dt = dh/dV * dV/dt
= 20/pih^2
dh/dt = 1/125 pi when h = 50
--------------------------------
Area = pi * h^2
Let area be A
dA/dt = 2pih * dh/dt
= 4/5 cm^2/s
--------------------
Surface area is area with the slant height. Remember that this cone is upturned so we are ignoring the pi * r^2.:
SA = pi * sqrt(2) * h^2
Let SA be a variable B
dB/dh = 2pi * sqrt(2)h
dB/dt = dB/dh * dh/dt
= 2pi sqrt(2) h * 1/125pi
Therefore dB/dt = 4/5sqrt(2)
Fair bit of algebra, feel free to proof-read it or check against answers. I haven't done related rates in a while but I am familiar with these type of questions.
dV/dt = 20 cm^3/s
Given parameters:
dV/dt = 20, find dh/dt, area and surface area.
V = pir^2 h^3/3
h = r as the angle is 45 degrees so tan45=1
Therefore
V = pi*h^3/3
dV/dh = pi * h^2
dh/dt = dh/dV * dV/dt
= 20/pih^2
dh/dt = 1/125 pi when h = 50
--------------------------------
Area = pi * h^2
Let area be A
dA/dt = 2pih * dh/dt
= 4/5 cm^2/s
--------------------
Surface area is area with the slant height. Remember that this cone is upturned so we are ignoring the pi * r^2.:
SA = pi * sqrt(2) * h^2
Let SA be a variable B
dB/dh = 2pi * sqrt(2)h
dB/dt = dB/dh * dh/dt
= 2pi sqrt(2) h * 1/125pi
Therefore dB/dt = 4/5sqrt(2)
Fair bit of algebra, feel free to proof-read it or check against answers. I haven't done related rates in a while but I am familiar with these type of questions.
