Respuesta :
hello
to solve this problem, we have to use the formula of volume of a rectangle
[tex]\text{volume}=\text{length}\times width\times height[/tex]but in this case, the value of the volume given is just 3/4 of the tank
if 3/4 of the tank is 14.4L, a full tank would be?
[tex]\begin{gathered} \frac{3}{4}=14.4L \\ 1=xL \\ \text{cross multiply both sides and solve for x } \\ 0.75=14.4 \\ 1=x \\ 0.75x=14.4 \\ x=\frac{14.4}{0.75} \\ x=19.2L \end{gathered}[/tex]the volume of the full tank would be 19.2L
let's use this information and solve for the height
but before we do that, we have to have a uniform S.I unit
convert the volume in L to cm^3
[tex]\begin{gathered} 1l=1000\operatorname{cm}^3 \\ 19.2L=x \\ x=\frac{19.2\times1000}{1} \\ x=19200\operatorname{cm}^3 \end{gathered}[/tex]we can now solve for the height of the rectangle
[tex]\begin{gathered} v=l\times w\times h \\ v=19200\operatorname{cm}^3 \\ l=40\operatorname{cm} \\ w=20\operatorname{cm} \\ 19200=40\times20\times h \\ 19200=800h \\ \text{divide both sides by coefficient of h} \\ \frac{19200}{800}=\frac{800h}{800} \\ h=24\operatorname{cm} \end{gathered}[/tex]from the calculations above, the height of the rectangle is 24cm
