A cylindrical tank has a diameter of 7 inches and a height of 51 inches. What is the volume of the tank? 

Step 1: write down the formula and identify the variables.

[latex]\Large \begin{array}{c} \text{volume of a cylinder} = {\text{diameter}}^{2} \times 0.7854 \times \text{height}\\ \textbf{Variables} \\ \text{height (h)} = 51 \text{ inches} \\ \text{diameter (d)} = 7 \text{ inches} \end{array}[/latex]

Now before we move on, check and make sure the variables are in similar units. If they are different, we’ll have to change them so they are both the same. 

Lucky for us, in this question they are both in inches so we are good to go.

Step 2: Plug the variables into the formula, and work through the question.

[latex]\Large \begin{array}{c} \text{volume} ={\text{d}}^{2} \times 0.7854 \times \text{h} \\ \text{volume}= 7 \text{ in} \times 7 \text{ in} \times 0.7854 \times 51 \text{ in} \\ \text{volume} = 1962.7 {\text{ in}}^{3}\end{array}[/latex]

Calculate the volume of a cylindrical tank that has a diameter of 555 millimetres and a height of 7.9 metres. 

Step 1: Write down the formula and identify the variables.

[latex]\Large \begin{array}{c} \text{volume of a cylinder} = {\text{diameter}}^{2} \times 0.7854 \times \text{height}\\ \textbf{Variables} \\ \text{height (h)} = 555 \text{ millimetres} \\ \text{diameter (d)} = 7.9 \text{ metres} \end{array}[/latex]

The height being 7.9 metres works for us but the diameter being 555 millimetres does not. We will have to change that to metres in order for everything to be consistent.

We will have to go back a few chapters and into our memory bank for this one.

Remember that 1 metre = 1000 millimetres.

To get the number of metres in 555 millimetres we do the following:

[latex]\Large \begin{array}{c} 1 \text{ metre} = 1000 \text{ millimetres} \\ \text{metres} = \dfrac{\text{number of millimetres}}{1000 \text{ millimetres/metre}} \\ \text{metres} = 0.555 \text{ metres} \end{array}[/latex]

Now that both of the variables are in similar units we can go ahead and solve for volume.

Step 2: Plug the variables into the formula and work through the question.

[latex]\Large \begin{array}{c} \text{volume} = {\text{d}}^{2} \times 0.7854 \times \text{h} \\ \text{volume} = 0.555 \text{ m} \times 0.555 \text{ m} \times 0.7854 \times 7.9 \text{ m} \\ \text{volume} = 1.91 {\text{ m}}^{3}\end{array}[/latex]

So we have our answer in cubic metres but what if wanted to change that answer to cubic millimetres? We’ll go back to our drawing of a cube to find out the relationship between cubic metres and cubic millimetres.

[latex]\Large \begin{array}{lc}\text{In metres:} & \text{volume} = \text{ side}\times \text{side} \times \text{side} \\ & \text{volume} = 1 \text{ m} \times 1 \text{ m} \times 1 \text{ m} \\ & \text{volume} = 1 {\text{ m}}^{3} \\ \text{In millimetres:} & \text{volume} = \text{ side} \times \text{side} \times \text{side} \\ & \text{volume} = 10 \text{ mm} \times 10 \text{ mm} \times 10 \text{ mm} \\ & \text{volume} = 1,000,000,000{\text{ mm}}^{3} \end{array}[/latex]

So in the end one cubic metre equals a lot of cubic millimetres More precisely one cubic metre equals one billion cubic millimetres.

So how many cubic millimetres are there in our cylindrical tank in the example above.

[latex]\Large \begin{array}{c} {\text{ mm}}^{3} = {\text{ mm}}^{3} \times 1,000,000,000 {\text{ mm}}^{3}{\text{/m}}^{3} \\ {\text{ mm}}^{3} = {1.91}^{3} \times 1,000,000,000 {\text{ mm}}^{3}{\text{/m}}^{3} \\{\text{ mm}}^{3} = 1,910,000,000 \end{array}[/latex]