Question

related rates ?

water flows into a giant basin at a constant rate of 7 cubic meters per minute. assume that the basin has a shape of a rectangular box with a square base. the base dimension is sqrt (5) meters. (assume water began flowing into the basin at t = 0 minutes). a) if the basin is full at 10 minutes, determine height of the basin. b) determine a formula for the volume V of the water in the basin after t seconds. c) determine a formula for the height h of the water in the basin as a function of time 't' d) determine dh/dt

Answer 1

a)

let the height of hasin be h

volume of the basin ,

amount water flown in 10 minutes = (7 m³/min)*(10 min)
=>amount water flown in 10 minutes = 70 m³

when basin is full V=70

=>5h=70
=>h=14

height of the basin is 14 meters

b)

volume of the water in the basin after t seconds ,V=7t

units are cubic meters

c)

V=5h,V=7t
=>5h=7t

units are meters

d)

units are meters per minute