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 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

Answer 1

@phi

Answer 2

this is the part I don't get ->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. <---

how can the sand in the cone be 3 times higher than the cone itself that contains it?

Answer 3

does this help @jdoe0001

Answer 4

I don't understand is there a formula or something

Answer 5

you need the volume of the cone
that has height 18 mm and radius 8 mm

also the volume of a cylinder that has height (54-18) mm and radius 8 mm

Answer 6

I see

Answer 7

here is how to find the volume of the cone
http://www.wikihow.com/Calculate-the-Volume-of-a-Cone

Answer 8

http://www.mathwarehouse.com/solid-geometry/cone/images/volume-cone-formula-vs-cylinder-base.png

Answer 9

use the formula
\[ V= \frac{1}{3} \pi r^2 h \]
I would leave the answer in terms of pi (because we will be dividing by the amount the sand is flowing out which is 10π cubic millimeters per second)

Answer 10

is the answer 268.8

Answer 11

yes

Answer 12

can you figure it out ?

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