qn (1 Viewer)

[bos1234]

Sand being poured from a conveyor belt froms a cone with height h and semivertical angle 60 degrees.Show that the volume of the pile is
V = πh³, and differentiate with respect to t.

Suppose that the sand is being poured at a constant rate of 0.3m³/min, and let A be the area of the base. Find the rate at which the height is increasing when
the radius is 4m



How do I do the ones in bold?

 

[ianc]

okay, a semivertical angle of a cone is the angle marked * in this triangle:

So you could write tan60=(r/h)
r=htan60

and then substitute for r in V=(1/3)pi(r²)h


The second part of the question is asking for an expression dh/dt, so you will have to look at what you have got and how you can manipulate it.
They give you dV/dt=0.3
Also, if you differentiate V with respect to h, you will get an expression for dV/dh.

So from this, you should be able to work out dh/dt = dV/dt * dh/dV

Now of course, you will get dh/dt in terms of h, so use the thing from the semivertical angle: r=htan60, and substitute for h.

Then susbstitute in r=4 to get your answer.



Hope this made sense!

 

[bos1234]

kk thanks for the diagram and soln.
got it now

is semivertical and apex mean the same thing?

bye