Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 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?
68.3 38.4 268.8 230.4

Question

Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 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?
68.3 38.4 268.8 230.4

jagr2713 · Answer

volume of the cone is 1/3 pi 8^2 * 18 = 64*6* pi 
volume of the cylinder is (54-18) * pi * 8^2 = 36*64*pi 
add up to get 
2688 pi

now divide by how fast the sand is leaving: 10 pi mm^3 / sec 
you get 268.8 secs