Related Rates: Quiz

Problem 2

An artificial garden pool is shaped like a hemisphere with depth equal to 0.75 meters. A gardener fills it with water at a rate of 0.5 liters per second.

  1. How long does it take to fill the pool?
  2. How fast does the water rise on average over the entire time it takes to fill the pool?

Answers, problem 2

  1. We first find the volume of the pool, defined as (4/3πr3)/2, where r is the radius of the hemisphere = 0.75 meters. Volume is therefore (4/3π0.753)/2 = 0.8836 cubic meters. To find the time it takes to fill the pool, we divide the volume by the rate at which the pool is being filled:

    0.8836 m * second/0.5liters * 1000 liters/m3 = 1767 seconds

  2. The rate at which the water rises = 0.75 meters/1767seconds = 0.042 centimeters per second

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