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, as shown below:
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

Answer 1

68.3
38.4
268.8
230.4

Answer 2

I think its 268.8

Answer 3

@Marcorie @misssunshinexxoxo @jdoe0001 @dan815

Answer 4

is their a pic?

Answer 5

Yes

Answer 6

@mathmate can you please help him

Answer 7

lol

Answer 8

sorry im not really sure try asking someone else i tried it and got the wrong answer

Answer 9

Thats okay :)

Answer 10

@Anon.

Answer 11

@slade

Answer 12

i agree with u @CaptainLlama49

Answer 13

Cool I just might have it right

Answer 14

Well you have the volume of the cylinder which is \[V = \pi r^2 h\] and cone is \[V_c = 1/3 \pi r^2h\]
we are given that the height of the hourglass is 18 mm, and the total height within the top portion of the hour glass is 54 mm.

It also tells us the radius of the cylinder and the cone is 8mm.
So we just need to find the total volume, using the formulas above and once we have that we can just divide by \[10 \pi~ mm^3\] to figure out the time it will take the sand to be at the bottom I assume?

Answer 15

yes

Answer 16

Yeah, so you should be able to figure out the rest

Answer 17

I got 268.8

Answer 18

Is that correct

Answer 19

Well lets find the volume of the cone and cylinder first, what did you get?

Answer 20

268.8

Answer 21

@Astrophysics

Answer 22

Well I don't really feel like doing the whole problem, I gave you the process you can plug in the numbers and check.

Answer 23

100% YES!

Answer 24

Haha, so it was right? :)

Answer 25

Yep

Answer 26

Nice work

Answer 27

Thank you :)