Solutions

1. \(1256.6 \text{ cm}^{3}\) (when using the pi button on the calculator)
2. \(288.63 \text{ in}^{3}\) (when using the pi button on the calculator)
3. \(426 \: {\text{m}}^{3}\) (when using the pi button on the calculator) (Written Solution)
   

   We are finding the volume of a water tower with a radius of 4.25 meters and a height of 7.5 meters, so we can use the formula for the volume of a right cylinder:

   \(\text{Volume} = {\text{π}} {\text{ r}}^{2}{\text{h}}\)

   The first thing we need to do is substitute or replace ‘r’ with 4.25 m and ‘h’ with 7.5 m

   \(\text{Volume} = {\text{π}}(4.25\:{\text{m}}){^{2}}(7.5\:{\text{m}})\)

   Next, we square \(4.25\: {\text{m}}\) to get \(18.0625 \:{\text{m}}^{2}\) (This means multiply \(4.25\:{\text{m}} \times 4.25\:{\text{m}}\).)

   \(\text{Volume} = {\text{π}}(18.0625\:{\text{m}}^{2})(7.5\:{\text{m}})\)

   Then we multiply \(18.0625 \:{\text{m}}^{2}\) by \(7.5\: {\text{m}}\), which gives us \(135.46875 \:{\text{m}}^{3}\). Remember \({\text{m}}^{2}\) times \({\text{m}}\) equals \({\text{m}}^{3}\) and tells us that we are measuring the volume in cubic meters.

   \(\text{Volume} = {\text{π}} 135.46875\:{\text{m}}^{3}\)

   Since we can multiply in any order, we can rewrite the equation like this, which is an acceptable mathematical answer:

   \(\text{Volume} = 135.47{\text{π}} \:{\text{m}}^{3}\) (Here we also rounded to the nearest hundredth place for simplicity.)

   We can also multiply 135.46875 by \({\text{π}}\) to get:

   \(\text{Volume} = 425.5876... {\text{m}}^{3}\)

   So the volume of the water tower is approximately \(426 \:{\text{m}}^{3}\) when rounded to the nearest whole number.

4. \(\text{Radius} = 11.25 \text{ in}\)
   \(\text{Volume} = 13319.86 \text{ in}^{3}\) (when using the pi button on the calculator) (Solution Video | Transcript)
5. \(113 \text{ ft}^{3}\) (when using the pi button on the calculator) (Written Solution)
   

   To find the volume of the column we can use the formula:

   \(\text{Volume} = {\text{π}} {\text{ r}}^{2}{\text{h}}\)

   The first thing we need to do is replace the ‘r’ with 1.5 ft and the ‘h’ with 16 ft.

   \(\text{Volume} = {\text{π}} (1.5\:{\text{ft}}){^{2}}(16\:\text{ft})\)

   Next, we need to square 1.5 ft. This means multiply 1.5 ft × 1.5 ft which equals \(2.25 \:{\text{ft}}^{2}\).

   \(\text{Volume} = {\text{π}} (2.25\:\text{ ft}^{2})(16\:\text{ft})\)

   Then we multiply \(2.25\: \text{ ft}^{2}\) by \(16\:\text{ft}\), which equals \(36\:\text{ft}^{3}\). Remember \(\text{ft}^{2}\) times ft equals \(\text{ft}^{3}\).

   \(\text{Volume} = {\text{π}} 36\:\text{ft}^{3}\)

   Since we can multiply in any order, we can rewrite the volume like this:

   \(\text{Volume} = 36{\text{π}}\:\text{ft}^{3}\)

   When we multiply 36 by \({\text{π}}\) we get:

   \(\text{Volume} = 113.0973... {\text{ft}}^{3}\)

   So the volume of the column is about \(113\: \text{ft}^{3}\) when rounded to the nearest whole number.

6. \(3853.3 \text{ mm}^{3}\) (when using the pi button on the calculator) (Solution Video | Transcript)