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.

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

The answer will be 62.4. We know this because of the next procedure:

We know that:

the volume of a cylinder is pi * r^2 * h

the volume of a cone is 1/3 * pi * r^2 * h

the total height is 47.

the height of the cone is 12.

the height of the cylinder must be 35.

Now, if the top half is filled with sand, then the volume of the sand is

pi * 4^2 * 36 and the volume of the cone is 1/3 * pi * 4^2 * 12.

the total volume = 1960.353816 cubic millimeters.

since the top drains at the rate of 10 * pi cubic millimeters per second, the top will be empty and the bottom full after 1960.353816 / (10 * pi) = 62.4 seconds.

I hope this answer is ok for you