Imprecise measurements - Math Central

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Quandaries & Queries

Question from Sara, a student:

Hi!
A water tank, in the shape of a cuboid (length 1.6 m, height 1.2 m, breadth 0.8 m), is full of water.
Water is drained from the tank at a rate of 8 litres per minute. The dimensions of the tank are given to the nearest 10 cm.
The rate at which the water is drained from the tank is given to the nearest 0.5 litres per minute.
(a) Calculate the smallest possible time to drain the tank.
(b) Calculate the greatest possible time to drain the tank.
Many thanks!!!

Hi Sara.

I'll show you how to do (a) and you will see how to do (b).

The time to drain the tank will be smallest when the amount of water is smallest and the drainage rate is highest.

So what is the highest drainage rate? Since the rate is rounded to the nearest 0.5 liter per minute, it could be as much as 8.25 liters per minute.

What is the smallest amount of water? It is the smallest volume cuboid, which means the cuboid with the smallest dimensions. Since the dimensions are rounded to the nearest 0.1 meters, the smallest cuboid would be 1.55 by 1.15 by 0.75, so the volume is 1.55 x 1.15 x 0.75 x 1000 liters per cubic meter, which is 1336.875 liters. Drained at a rate of 8.25 liters per minute, that takes 1336.875/8.25 = 162.05 minutes.

Cheers,
Stephen La Rocque.

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