Question

A chemical factory has 2 cylindrical chemical tanks, one containing Chemical X and the other containing Chemical Y. The tank containing Chemical X occupies a space of 25 ft.3 and contains 1.5 times more Chemical X than the tank containing Chemical Y. The base area of the tank containing Chemical Y is 3.2 ft.2. What is the approximate height of the tank containing Chemical Y? Round to the nearest tenth. (Use 3.14 for π .)

Answer 1

The tank with Chemical X "takes up" a space of 25ft³.  Ordinarily we think of something "taking up" space as being area or surface area; however, area is a square measurement, and this is cubic; this must be volume.  The volume of the tank with Chemical X is 1.5 times the volume of the tank containing Chemical Y; setting this up in an equation we would have
25 = 1.5V
We would divide both sides by 1.5 to get the volume of the tank containing Chemical Y:
$\frac{25}{1.5}=\frac{1.5V}{1.5} \\16 \frac{2}{3}=V$
To find the volume of a cylinder, we find the base area and multiply by the height.  We know the volume and we know the base area, so our equation to find the height of the tank containing Chemical Y would look like:
$16 \frac{2}{3}=3.2h \\ 16 \frac{2}{3}=3 \frac {2}{10}h$
We would now divide both sides by 3 2/10:
$\frac{16 \frac{2}{3}}{3 \frac{2}{10}}= \frac{3 \frac{2}{10}h}{3 \frac{2}{10}}$
This is the same as:
$\frac{\frac{50}{3}}{\frac{32}{10}}=h \\ \\ \frac{50}{3}* \frac{10}{32}=h \\ \\ \frac{500}{96}$
So the height of the tank containing Chemical Y is 500/96 = 5 5/24 feet.