Question

`\underline{ \text{Question}} :` In the given figure , a cubical vessel of length 10 cm is completely filled with water. If the water is poured into a rectangular vessel of length 25 cm , breadth 20 cm and height 10 cm. Find the height of the water level in the rectangular vessel. How much more water is required to fill the rectangular vessel completely ? ( 1 l = 1000
`\sf{ {cm}^(3) }` .

⭒Thanks in advance ツ ! ⭒

Answer 1

Part A)

The height of the water level in the rectangular vessel is 2 centimeters.

Part B)

4000 cubic centimeters or 4 liters of water.

Explanation:

We are given a cubical vessel that has side lengths of 10cm. The vessel is completely filled with water.

Therefore, the total volume of water in the cubical vessel is:

`V_(C)=(10)^3=1000\text{ cm}^3`

This volume is poured into a rectangular vessel that has a length of 25cm, breadth of 20cm, and a height of 10cm.

Therefore, if the water level is h centimeters, then the volume of the rectangular vessel is:

`V_R=h(25)(20)=500h\text{ cm}^3`

Since the cubical vessel has 1000 cubic centimeters of water, this means that when we pour the water from the cubical vessel into the rectangular vessel, the volume of the rectangular vessel will also be 1000 cubic centimeters. Hence:

`500h=1000`

Therefore:

`h=2`

So, the height of the water level in the rectangular vessel is 2 centimeters.

To find how how much more water is needed to completely fill the rectangular vessel, we can find the maximum volume of the rectangular vessel and then subtract the volume already in there (1000 cubic centimeters) from the maximum volume.

The maximum value of the rectangular vessel is given by :

`A_(R_M)=20(25)(10)=5000 \text{ cm}^3`

Since we already have 1000 cubic centimeters of water in the vessel, this means that in order to fill the rectangular vessel, we will need an additional:

`(5000-1000)\text{ cm}^3=4000\text{ cm}^3`

Sincer 1000 cubic centimeters is 1 liter, this means that we will need four more liters of water in order to fill the rectangular vessel.