How would I find out what the height of the pile would be after 5 minutes?
A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. The volume formula for a right circular cone is V= 1/3 πr^2h.
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Also how would I figure out how fast the pile is increasing? ..I don't really understand whats the difference from finding the actual height after five minutes or how fast it is increasing.
you know that h = 2d = 4r. So, the volume v is
v = 1/3 pi r^2 h = 4/3 pi r^3
to find the height after 5 minutes, just recall that the volume will be 5min * 20m^3/min = 100 m^3
So, just solve for h (4r) when v = 100
To find how fast the pile is increasing, recall that
dv/dt = 4pi r^2 dr/dt = pi r^2 dh/dt
and you know that dv/dt = 20
v = 1/3 pi r^2 h = 4/3 pi r^3
to find the height after 5 minutes, just recall that the volume will be 5min * 20m^3/min = 100 m^3
So, just solve for h (4r) when v = 100
To find how fast the pile is increasing, recall that
dv/dt = 4pi r^2 dr/dt = pi r^2 dh/dt
and you know that dv/dt = 20
2 answers