Question

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?

Answer 1

said from the person above, the answer is 126 seconds.

The reasoning is because all of you don't even divide by 10.

10(pi) cubic mm = 10(pi)^3 therefore allowing you to ignore the symbol (pi)

Answer 2

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.