An open tank is in the form of the right circular cone with

An open tank is in the form of the right circular cone with vertex down.The radius of the tank is five feet and the altitude is ten feet. If the water evaporates from the tank at a rate which is proportional to the exposed surface area (dv/dt=kA) and the depth decreases from ten feet to five feet in twenty days, when will the depth be two feet?

Solution

when water decreases from 10 feet to 5 feet then the radius at 5 feet would be 2.5

here the question is when will be the depth be 2 feet it means from bottom it should be 2 feet considering from center that is after evaporation it should be 3 feet and radius at 3 feet is 1.25

here 2.5 radius and 5 feet depth = 20

but for 1.25 radius and 3 feet = ?

by cross multliplication = 6 days we will get

so the final answer is 6 days for depth 2 feet.