Question

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? (4 points)

Answer 1

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 * 36

volume (cone) =  1/3 * pi * 4^2 * 12

Total volume = 1960.353816 cubic millimeters

353816 / (10 * pi) = 62.4 seconds.

It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass.