Respuesta :
Given:
Dimensions of a tank are 50 cm by 32 cm by 20 cm
The tank is full of water and sand
Ratio of volume of water to the volume of sand is 5:1
To find:
Volume of water in the tank in liters
Solution:
Without loss of generality, let,
Length of tank = 50 cm
Breadth of tank = 32 cm
Height of tank = 20 cm
Then, we have,
Total Volume of the tank = Length * Breadth * Height
[tex]\Rightarrow[/tex] Total Volume = 50*32*20 cc
[tex]\Rightarrow[/tex] Total Volume = 32000 cc
It is given that,
Volume of water : Volume of sand = 5:1
[tex]\Rightarrow[/tex] (Volume of water)/(Volume of sand) = 5/1
Cross multiplying, we have,
Volume of sand = (Volume of water)/5
It is also given that the tank is full of water and sand. This implies that,
Volume of water + Volume of sand = Total Volume
Using the value, we obtained, we get,
Volume of water + (Volume of water)/5 = Total Volume
[tex]\Rightarrow[/tex] (6 * Volume of water)/5 = Total Volume
Plugging in the value of total volume, we get,
[tex]\Rightarrow[/tex] (6 * Volume of water)/5 = 32000 cc
[tex]\Rightarrow[/tex] Volume of water = [tex]\frac{32000*5}{6}[/tex] cc
[tex]\Rightarrow[/tex] Volume of water [tex]\approx[/tex] 26,666.6667 cc
We know that,
1 cc = 0.001 liters
[tex]\Rightarrow[/tex] 26,666.6667 cc = (26666.6667 * 0.001) liters
[tex]\Rightarrow[/tex] 26,666.6667 cc [tex]\approx[/tex] 26.667 liters
Thus, Volume of water in the tank is approximately 26.667 liters
Final Answer:
Volume of water in the tank (in liters) is approximately 26.667 liters
