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 15 millimeters. the total height of the sand within the top portion of the hourglass is 45 millimeters. the radius of both cylinder and cone is 6 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 answer is 126 s

(1) Calculate the volume of the sand.
The volume of the sand is: V = V1 + V2
V1 - the volume of the cone with height 15mm and radius 6mm
V2 - the volume of the cylinder with height 30 mm (45mm of sand - 15 mm of cone) and radius 6mm

V1 = 1/3 πr²h1
V2 = πr²h2
V = 1/3 πr²h1 + πr²h2

r = 6 mm
h1 = 15mm
h2 = 30 mm

V = 1/3 π * 6² * 15 + π * 6² * 30
V = 1/3 π * 36 * 15 + π * 36 * 30
V = 180π + 1080π
V = 1260π mm³

(2) Calculate how many seconds will it take until all of the sand has dripped to the bottom of the hourglass:
10 π mm³ is per 1 sec
1260 π mm³ is in x sec

10π : 1s = 1260π : x
x = 1260π * 1s / 10π
x = 126 s