To determine how many litres of water a cubical water tank that is 1.2 meters high can hold, we can follow these steps:
1. Calculate the Volume of the Cube:
A cubical water tank has all sides of equal length. Given that the height of the tank is 1.2 meters, this means each side of the cube is also 1.2 meters long. The formula for the volume of a cube ([tex]\(V\)[/tex]) is:
[tex]\[
V = \text{side}^3
\][/tex]
Substituting the side length of 1.2 meters into the formula gives:
[tex]\[
V = (1.2)^3
\][/tex]
Calculating this, we get:
[tex]\[
V = 1.728 \text{ cubic meters}
\][/tex]
2. Convert Cubic Meters to Cubic Centimeters:
To further convert the volume from cubic meters to cubic centimeters, we use the fact that [tex]\(1 \text{ cubic meter} = 1,000,000 \text{ cubic centimeters}\)[/tex]. Thus,
[tex]\[
V_{\text{cm}^3} = 1.728 \text{ cubic meters} \times 1,000,000 \text{ cm}^3/\text{m}^3
\][/tex]
Carrying out this multiplication, we get:
[tex]\[
V_{\text{cm}^3} = 1,728,000 \text{ cubic centimeters}
\][/tex]
3. Convert Cubic Centimeters to Litres:
We know that [tex]\(1 \text{ liter} = 1,000 \text{ cubic centimeters}\)[/tex]. Therefore, to convert the volume from cubic centimeters to litres:
[tex]\[
V_{\text{litres}} = \frac{1,728,000 \text{ cm}^3}{1,000 \text{ cm}^3/\text{litre}}
\][/tex]
Simplifying this, we get:
[tex]\[
V_{\text{litres}} = 1,728 \text{ litres}
\][/tex]
Hence, the cubical water tank, which is 1.2 meters high, can hold 1,728 litres of water.
