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

Answer 1

68.3

38.4

268.8

230.4

Answer 2

Calculate the volume of the cone portion.
Calculate the volume of the cylindrical portion.
Add those up to get the total volume of sand.
Divide that volume by the rate the sand flows to get the time it takes.

Answer 3

is it a?

Answer 4

Give that a try and ask me questions when you get stuck. By the way, the formula for the volume of a cone is:
\[\frac{1}{3}\pi*r^2h\]
where r is the radius and h is the height
And the formula for volume of a cylinder is
\[\pi*r^2h\]
where r is the radius and h is the height.

And I'm not going to answer any guesses unless you give some of your work. Sorry.

Answer 5

ok thank you, i had the volume for the cone incorrect

Answer 6

Why did you delete your post? It looked right to me. I was about to check the numbers.

Answer 7

1206.14 for volume of cone, 3620.57 for volume of cylinder

Answer 8

1206.86 i mean

Answer 9

Your volume for the cone is correct. Check your work on the cylindrical part. The tricky part for these is making sure you're using the right things for radius and height.