Question

Each cone of the hourglass has a height of 18 millimeters . the total height of the sand within the top portion of the hour glass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top to the bottom at a rate of 10n cublic millimeters per second. How many seconds will it take until all the sand has dripped to the bottom of the hour glass?

Answer 1

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