Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass? ..... I really need help with this one please and thank you :)

Question

sirm3d · Answer

let's  begin with the volume of the cone. do you know the formula for the volume of a cone?

anonymous · Answer

v=1/3 pi r2 h? right

anonymous · Answer

are you still there?

anonymous · Answer

68.3 

 38.4 

 268.8 

  230.4

are the possible answers yet i keep gettin 85.78 i really dont understandthis

sirm3d · Answer

yes i am. sorry, i am also working on another problem.
we know that sand drips at a rate of 10pi cu. mm./sec, and this value is $$dV/dt$$

sirm3d · Answer

this given requires us to differentiate the volume function with respect to time. right?

anonymous · Answer

could you dum that down a little bit please?

sirm3d · Answer

sorry, this is not a calculus problem. my mistake.

anonymous · Answer

can you still help me solve it?

sirm3d · Answer

something is wrong with the given. the height of the cone is 18 mm and that of the sand within the top pile is 54 mm. can you check the facts?

anonymous · Answer

Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?  that is the exact question i was given

sirm3d · Answer

i have a problem fiiting sand of height 54 mm within a cone that is just 18 mm in height.

sirm3d · Answer

for solution's sake, let us just assume that the height of sand is just 5.4 mm and not 54 mm.

anonymous · Answer

this is the picture and both cones are 18 i belive

anonymous · Answer

wont doing the equation with 5.4 in plave of 54 mess up the orignal equation?

sirm3d · Answer

|dw:1352075550576:dw|

sirm3d · Answer

the problem is pysically impossible. the cone can only hold sand to a height of 18mm, but the problem states that the height of the sand is more than that. do you see now the problem with the given?

anonymous · Answer

yes i understand it is impossible but then agian it is math and can trualy be illogical can we just try to solve for the given?

anonymous · Answer

do you see the picture i uploaded?

sirm3d · Answer

yes i do. wait a minute. i'll recheck my solution.

sirm3d · Answer

ok, the answer is among the choices.
the sand occupies the entire cone and portion of the cylinder.

sirm3d · Answer

so we're going to need two formulas. (1) volume of cylinder, and (2) volume of cone. do you known the formula for (1)?

anonymous · Answer

ummmm i belive it is pi r2h

sirm3d · Answer

good. let's identify the radius and height of the two solids. the radiuii are the same and it's 8 mm. what about the height of each solid?

anonymous · Answer

its 18 correct?

sirm3d · Answer

that's for the cone. what about the cylinder?

anonymous · Answer

oh i dont know how to find that o_O

sirm3d · Answer

here's the solution. the total height of the sand in the cylinder and the cone is 54 mm and 18 mm for the cone ONLY. can you compute the height of the sand in the cylinder now?

anonymous · Answer

36 correct?

sirm3d · Answer

good. now plug the correct height in the formula for each solid. the total volume of sand you'll get is

anonymous · Answer

pi*8^2*18? which would be 3619.11

sirm3d · Answer

18 is the height of the cone but the formula you used is that of the cylinder. the volume of the cylinder is $$\pi*8^2*36$$

anonymous · Answer

oh ahaha sorry, 7238.2294

sirm3d · Answer

get the volume of the cone and add them up for the total volume of the sand.

anonymous · Answer

would you find the cone by 1/3*8^2*36?

sirm3d · Answer

the height of the cone is 18, that of the cylinder is 36. you are getting them mixed up. be careful next time.

anonymous · Answer

ok so it should be 1/3*8^2*18 which is 384

anonymous · Answer

wait i forgot to multiply pi

sirm3d · Answer

there's still the pi in the formula.

sirm3d · Answer

ahaha. you noticed it too.

anonymous · Answer

1206.371

sirm3d · Answer

for the final part. add the volumes and divide the total by the rate by which the sand drips. you should get the correct answer now.

anonymous · Answer

8444.6004 is the two volumes added but how do i get the rate at which the sand drops?

sirm3d · Answer

the problem says sand drips at the rate of 10 pi cu. mm. per sec.

anonymous · Answer

waite i forgot it drops at a rate of 1o pi but when i divided by such i got 2652.949458 which isnt on the answers given

sirm3d · Answer

perhaps you did it wrong in the calculator. you should have used parenthesis to enclose 10*pi, like this:
8444.6004/(10*3.1416)

anonymous · Answer

i didnt use parentheses let me try it now with that tip

anonymous · Answer

i got 268.799

sirm3d · Answer

cheers. =)
if you are not sure when to use paretheses in fractions, i suggest you compute the parts of the fraction separately.

anonymous · Answer

ok i will keep that in mind thankyou soooo much for the help :D

sirm3d · Answer

you're welcome. come back if you have other questions.