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?

The solution would be like this for this specific problem:

Volume of a cylinder = pi * r^2 * h 

Volume of a cone = 1/3 * pi * r^2 * h 

Total Height = 47

Height of the cone = 12

Height of the cylinder = 35

If the top half is filled with sand, then:

volume (sand) = pi * 4^2 * 36

volume (cone) =  1/3 * pi * 4^2 * 12

Total volume = 1960.353816 cubic millimeters

353816 / (10 * pi) = 62.4 seconds.

It will take 62.4 seconds until all of the sand has dripped to the bottom of the hourglass. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

last option

step-by-step explanation:

given that δdef is right and isoceles,

assuming that side df is the hypotenuse means that de an ef are the other 2 sides that intersect at 90° and are of equal length.

because they are of equal length, we can say that they are congruent

because they intersect at 90°, their slopes must be opposite reciprocals.

only the last option satisfies these conditions.

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5