Question

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder.


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Each cone of the hourglass has a height of 15 millimeters. The total height of the sand within the top portion of the hourglass is 45 millimeters. The radius of both cylinder and cone is 6 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?

Answer 1

Calculate the volume of sand, the cone will be completely filled and the cylinder will have sand up to the 30 mm level.
Volume of sand will = the volume of the cone: 1/3 * pi * (6 mm)^2 * 15 =
1/3 * pi * 36 * 15 =180 pi cubic mm the cylinder will have a volume of sand equal to:
pi * (6 mm)^2 * 30 mm=pi * 36 sq mm * 30 mm=1080 pi cubic mm.
The total sand is the sum: 1080 pi cubic mm +180 pi cubic mm = 1260 pi cubic mm.

Answer 2

how many seconds

Answer 3

the sand travels at a rate of 10 pi/sec so the sane will take (1260 pi)/10 pi/sec=
=126 pi seconds.

Answer 4

your the best!

Answer 5

Always check to be sure, I am subject to err on occasions lol.. But I think that is it. Good luck with your studies.

Answer 6

@radar how did you calculate the volume of the sand to get 30?

Answer 7

@Ghostbird. The steps that I used are provided in the post. First was calculated the volume of the cone (which was completely filled). Using the equation for the volume of a cone. this resulted in a value of 180 pi cubic mm. Is this the one you are questioning?

Then the volume of a cylinder was calculated. Note the height within the cylinder was 30 mm as the total height was 45 mm and the cone was 15 mm high. This resulted in a volume of 1080 cubic mm. Is the calculation you are questioning?

As I said the math needs verifying I may have made an error, ....