Answer to Question #124940 in Geometry for Jonathan

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, 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

Answer 1

Solution.

The solution would be like this for this specific problem:

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

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

Total Height = 47;

Height of the cone = 12;

Height of the cylinder = 35;

If the top half is filled with sand, then:

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

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

Total volume = 1960.353816 cubic millimeters

353816 / (10 * $\pi$ ) = 62.4 seconds.

Answer: 62.4s.