Wheat runs from a hole in a silo at a constant rate and forms a conical heap whose base is triple the height. If after 1 minute, the height of the heap is 20cm, find the rate at which the height is rising at this instant. [Volume Cone= 1/3*pi*r^2*h ]
Find the total volume of the cone right now (after 1 minute) using the formula and knowing that the height = 20cm and the base = 3x20cm Then, find the rate of the flow from the silo (volume found above, divided by time - or 1 minute) to get rate in cm^3/minute This is the rate for the whole cone - so you have to figure out the rate for just the height (cm/minute). Not exactly sure how to do that.
base=b, height=h, radius of cone at base=r given b=3h b=2r so 2r=3h or r=(3/2)h V = (1/3)πr?h = (1/3)π((3/2)h)?h = (3/4)πh? V'= (9/4)πh?h' and given h' = 20/1 or 20 cm/min then V' = (9/4)π(20?)20 = 18000π
