Question

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
- 8.5
-56.0
- 62.4

Answer 1

Before you know the time it takes to empty the upper part, you need to know the volume of sand in it. This volume is composed of both figures, the cone + the cylinder.
the volume of the cylinder is the area of the base times the height, so pi*r^2*h
pi*4^2*(47-12) = 560pi mm^3
Can't remember the formula for volume of a cone, would you have it per chance?

Answer 2

1/3TTr^2 (h)

Answer 3

good, so 1/3 * pi * 4^2 * 12 = 64 pi
your total volume is 560 pi + 64 pi = 624 pi
So, now you know that, each second, 10pi mm^3 of sand fall in the bottom part. How would you do to find out how long it will take for your hourglass to empty?

Answer 4

divide by 60?

Answer 5

i really dont know

Answer 6

Ok, let's rewrite it this way, maybe that'll ring a bell :
\[10pi / 1 \sec = 624 pi / x \sec\]
We need to find x here

Answer 7

Can you find the total volume of the hourglass?

The hourglass looks like:



Sorry, the diagram is not to scale, the cylindrical portion should have been longer.