Question

A rectangular tank is 3/4 filled with water. there are 14.4 L of water in the tank. what is the height of the tank?Width: 40cmLength: 20 cmHeight: unknown Options:A= 16cm B= 20cm C= 24 cmD= 28cm(the question is asking for height of the whole height, not just 3/4)

Answer 1

Since the tank is filled up to 3/4 of its maximum volume and this represents 14.4 liters of water, we have the following equation:

$\frac{3}{4}\cdot V=14.4$

where V represents the total volume of the tank. Since we have the measure of the width and the length in cm, we can convert 14.4 in cm^3 to get the following:

$14.4l=14400cm^3$

Now, we know that the formula for the volume of a rectangular prism is:

$V=w\cdot l\cdot h$

where w,l and h represent the width length and height respectively. Substituting the values that we have,we get the following equation:

$\begin{gathered} \frac{3}{4}V=14400 \\ \Rightarrow0.75w\cdot l\cdot h=14400 \\ \Rightarrow0.75(40)(20)h=14400 \\ \Rightarrow600h=14400 \\ \Rightarrow h=\frac{14400}{600}=24 \\ h=24\operatorname{cm} \end{gathered}$

therefore, the height of the tank is 24 cm