Chapter 13.4, Problem 1P

A tank in the shape of a rectangular prism has a base that is 20 cm wide and 30 cm long. The tank is partly fllIed with water. When a rock is put in the tank and sinks to the bottom, the water level in the tank goes up 2 cm. What is the volume of the rock? Explain your reasoning. See above

To determine

To find:The volume of the rock such that rock placed in the partly filled rectangular tank $20$ cm wide and $30$ cm long raises the water level in the tank by $2$ cm.

Answer to Problem 1P

The volume of the rock such that rock placed in the partly filled rectangular tank $20$ cm wide and $30$ cm long raises the water level in the tank by $2$ cm $1200\text{ cu}\text{.cm}$ .

Explanation of Solution

Given information:

The rock placed in the tank raises the water level in the tank by $2$ cm.

Calculation:

The rock is put into the tank and it sinks to bottom as a result the water level in the rectangular tank rises by $2$ cm that means the rock displaces a certain volume of water and this volume of water displaced can be calculated as below.

  $\begin{array}{c}\text{Volume of water}=\left(\text{length}\right)\cdot \left(\text{width}\right)\cdot \left(\text{rise in water level}\right)\\ =30\cdot 20\cdot 2\\ =1200\text{ cu}\text{.cm}\end{array}$

Now, the volume of the water displaced due to the submergence of rock must be equal to the volume of the rock.

Hence, the volume of the rock is $1200\text{ cu}\text{.cm}$ .

Conclusion:

The volume of the rock such that rock placed in the partly filled rectangular tank $20$ cm wide and $30$ cm long raises the water level in the tank by $2$ cm is $1200\text{ cu}\text{.cm}$ .