Volume of Submersed Objects

Question

A fish tank in the shape of a rectangular prism is 1 m long and 30 cm wide. The tank is 1/2 full. Then 30 liters of water are poured into the tank as it then becomes 2/3 full. How tall is the tank? Explain your reasoning.

Answer 1

The volume of the tank is:

 

V = length*width* height

 

The length is 1 m, the width = 30 cm = 0.3 m

 

V = (1 m)*(0.3 m)*height = (0.03 m²)*height

 

We need one more piece of information to solve for the height.  The tank is 1/2 full. Then 30 liters of water are poured into the tank and it then becomes 2/3 full.  So (2/3)V - (1/2)V = 30 liters

 

(2/3)V - (1/2)V = 30 liters

(4/6)V - (3/6)V = 30 liters

(1/6)V = 30 liters

V = 30*6 = 180 liters

 

Now we can find the tank's height.  But first note that one liter = (10 cm)*(10 cm)*(10 cm) = (0.1 m)*(0.1 m)*(0.1 m) = 0.001 cubic meters.  So 180 liters = 180*(0.001) = 0.180 m³:

 

0.180 m³ = (0.3 m²)*height

0.180/(0.3) = height

0.6 m = height