Volume of submersed objects versus weight of floating objects

Question

A tank in the shape of a rectangular prism is 50 cm tall, 80 cm long and 30 cm wide. First, some rocks are placed at the bottom of the tank. Then 80 liters of water are poured into the tank. At that point, the tank is 3/4 full. What is the total volume of the rocks in cubic meters? Explain your reasoning.

Answer 1

50 cm * 80 cm * 30 cm = 120000 cm³

1 cm³ of water = 1 mL of water

120000 / 1000 = 120 L

So the tank holds 120 L without anything else.

 

80 / 120 = x

8 / 12 = x

2 / 3 = x

So 80 L normally fills the tank 2/3 the way full

 

2/3 + R = 3/4

8/12 + R = 9/12

R = 1/12

So the rocks fill 1/12 of the tank.

 

120 L / 12 = 10

So 1/12 of the tank is 10L

10 L * 1000 ^mL/_L = 10,000 mL

Remember, 1 mL = 1 cm³

 

So the rocks' total volume is 10,000 cm³.