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?

Question

anonymous · Answer

by total height =47 do you mean volume?

anonymous · Answer

no it says just the height of the sand in the glass

anonymous · Answer

it doesn't make sense because 47 is larger than 12 which is listed as the height of the hourglass... but if you can get the sand part into cubic mm's then you just divide the rate by the cubic mm's

anonymous · Answer

I still dont understand it

anonymous · Answer

these are the choices they give me  6.4 

 62.4 

 8.5 

 56.0

anonymous · Answer

if you take the volume of the sand in the cone (Volume of a cone =1/3*pi*r*r*h) and divide by the rate you will get units of mm/(mm/s)=seconds.
If you ignore the 47, the volume of the top cone is 1/3*pi*16*12=200.96.
when i divide that by the rate i get 200.96mm/(31.4mm/sec) =6.4seconds