Each cone of the hourglass has a height of 15 millimeters. the total height of the sand within the top portion of the hourglass is 45 millimeters. the radius of both cylinder and cone is 6 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?

Calculate the volume of sand, the cone will be completely filled and the cylinder will have sand up to the 30 mm level.

Volume of sand will = the volume of the cone:
= 1/3 * pi * (6 mm)^2 * 15
= 1/3 * pi * 36 * 15 =180 pi cubic mm

the cylinder will have a volume of sand equal to:
= pi * (6 mm)^2 * 30 mm
= pi * 36 sq mm * 30 mm 
= 1080 pi cubic mm

The total sand is the sum:
= 1080 pi cubic mm +180 pi cubic mm
= 1260 pi cubic mm.