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

Question
Answer:
Let
Vco------------------- >Volume cone
Vcy------------------ >Volume cylinder 
r= 8mm
hco----------- > height of cone=18 mm
hcy------------ > height of cylinder =54-18=36 mm
then
Vco=π*r² *hco/3--------- > π*8² *18/3=π*384 mm³

Vcy=π*r² *hcy--------- > π*8² *36=π*2304 mm³

the total cubic millimeters of sand=Vco+Vcy=π*384+π*2304=π*2688

if 10π cubic millimeters --------------------- > 1 seg
π*2688--------------------------------- X
x=π*2688/10π=268.8 seg

the answer is 268.8 seg
solved
general 11 months ago 5528