Question

Containment System. Holding tanks for hazardous liquids are often surrounded by containment tanks that will hold the hazardous liquid if the main tank begins to leak. In the graphic below, the center tank has a height of 16 feet and a radius of 6 feet. The outside containment tank has a height of 4 feet and a radius of 8 feet. If the center tank is full of heating fuel and develops a leak at the bottom, will the containment tank be able to hold all the heating fuel that leaks out?

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

Part A:

The volume of the holding tank=

`\begin{gathered} \text{Volume of the cylinder}=\text{ }\pir^2h \\ \text{where }\pi\text{ = }(22)/(7) \\ r\text{ = 6 f}eet \\ \text{h = 16 f}eet \end{gathered}`

Volume of the cylinder=

`\begin{gathered} (22)/(7)\text{ X 6 X 6X 16} \\ =\text{ }(12672)/(7) \\ =\text{ 1810.2857} \\ \cong1810.29ft^3(\text{ to 2 decimal places)} \end{gathered}`

Step 3:

Part B:

The volume of the containment tank=

`\begin{gathered} \pi r^2h \\ \text{where }\pi=(22)/(7) \\ r\text{ = 8 f}eet \\ h\text{ = 4 fe}et \end{gathered}`

Hence,

`\begin{gathered} (22)/(7)\text{ X 8 X 8 X 4} \\ =\text{ }(5632)/(7) \\ =\text{ 804.5714} \\ \cong804.57ft^3\text{ ( to 2 decimal places)} \end{gathered}`

Step 4:

Part C:

If the center tank is full of heating fuel and develops a leak at the bottom, will the containment be able to hold all the heating fuel that leaks out?

Answer: NO