Question #124940

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, as shown below:


Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 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?


6.4

62.4

8.5

56.0


1
Expert's answer
2020-07-06T20:30:12-0400

Solution.

The solution would be like this for this specific problem:


Volume of a cylinder: =πr2h= \pi * r^2 * h ;


Volume of a cone =1/3πr2h;= 1/3 *\pi * r^2 * h;


Total Height = 47;


Height of the cone = 12;


Height of the cylinder = 35;


If the top half is filled with sand, then:


volume (sand) =π4235;= \pi * 4^2 * 35;


volume (cone) =1/3π4212;= 1/3 *\pi * 4^2 * 12;


Total volume = 1960.353816 cubic millimeters


353816 / (10 * π\pi ) = 62.4 seconds.

Answer: 62.4s.



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