Question

@ Sand is pouring out of a chute at a rate of 8 cubic feet per minute. It is landing in a pile that is (roughly) in the shape of a cone with the diameter always being twice the height. How fast is the diameter expanding when the diameter is 20 feet wide? How would the answer change if the diameter was always three times the height-and, everything else was the same? (Give exact answer, and approximate rounded to nearest hundredth!)

Answer 1

het de is rading of cone & his height of cone Vis the volume of cone given diameter = 2h = 2h sand is pouring from chute is 8 ft/min de = 8 ft/min we have com's volume = Trith V= / h v= (E3th h = V = 1 h v = TPM =퓨을 품을 쟤 VF 얘 diff w. n. to it - T. 30² de 29

given ( = 20 oft wide de a = 0.05092 ft/min af PER diameter is 3 times the height d = 3h = 3h v= 1T xc = They? xf = diff were to it get 8-264 8 = I x 3 x 20 x de de = - = 0.0763 ft/min 757