The storage shed shape of a half-cylinder of radius r and length l.

The shed is filled with sawdust whose density (mass/unit volume) at any point is proportional to the distance of that point from the floor. The constant of proportionality is k. Calculate the total mass of sawdust in the shed.

Question

The storage shed shape of a half-cylinder of radius r and length l.

The shed is filled with sawdust whose density (mass/unit volume) at any point is proportional to the distance of that point from the floor. The constant of proportionality is k. Calculate the total mass of sawdust in the shed.

koikkara · Answer

So, here as per the question, The shed is filled with sawdust whose density at any point is proportional to the distance of that point from the floor. the constant of proportionality is k. calculate the total mass of sawdust in the shed. Volume of the Shed = (πr² /2 )l Given: Density = kd ,d = distance from the floor Density = Mass (M) / Volume kd = M / (πr² /2)l M = π r² l / 2 (kd) >>>>> M = π l r² kd/2 << Ans....... well...i think this is it....lol

anonymous · Answer

its a half cylinder so volume is πr^2l / 2

anonymous · Answer

my problem is that i dont know how to find "d"

anonymous · Answer

mass = πr^2l/2 *k*d(distance from floor)

anonymous · Answer

I need to figure out what the distance from the floor is

koikkara · Answer

density (mass/unit volume)

anonymous · Answer

and density = k * (distance from floor)

koikkara · Answer

well, it may help than i could.... http://mathforum.org/kb/message.jspa?messageID=688054

koikkara · Answer

hope that defines evrythin....

anonymous · Answer

doesn't explain how to find "d" :(

koikkara · Answer

well, one user is there who can explain them...his name is "In Your Head"....he can sort out, as i rembr only some formulas and not in detail...well, i passed out 12th...4yrs ago...

koikkara · Answer

@Ldaniel ...ask...user named..."In Your Head"...

anonymous · Answer

@inyourhead

anonymous · Answer

help me please

anonymous · Answer

there might be some integration needed.

anonymous · Answer

ok this is what i have so far

$$Volume = \frac{\pi*r^{2}*L}{2}$$
$$Density = kd$$
$$Density = \frac{mass}{volume}$$
$$kd = \frac{mass}{\frac{\pi*r^{2}*L}{2}}$$
$$mass = \frac{2*k*d}{\pi*r^{2}*L}$$

anonymous · Answer

still you didn't find d

anonymous · Answer

true.  however, I believe that some calculus is needed as Koikkara's link shows.

anonymous · Answer

this may help http://mathhelpforum.com/calculus/130945-finding-mass-density-volume.html