When we find the volume of a rectangular object, we find the area of the base and multiply it by the height. We do the same thing to find the volume of a cylinder only this time the base is a circle. We find the area of the base \( \pi r^2 \) and multiply that by the height of the cylinder. Here is some vocabulary to help with this lesson.

• Right Angle = This is the same thing as perpendicular, two lines come together at 90 degrees like the corner of a rectangle.
• Right Circular Cylinder = A shape like a tube, the ends (or base) form a circle and the sides are perpendicular to the base.

Video Source (05:54 mins) | Transcript

Let \( r = radius \) and \( h = height \)

\( Volume\:\ of\:\ a\:\ Right\:\ Circular\:\ Cylinder = \pi r^2h \)

Additional Resources

• Khan Academy: Cylinder Volume (8:06 mins; Transcript)

Practice Problems

1. A can of food is a right circular cylinder with a radius of 5 cm and a height of 16 cm. Find the volume of the can. Round your answer to the nearest tenth. (
   Solution

   x

   Solution:
   \(1256.6 \text{ cm}^{3}\) (when using the pi button on the calculator)
   )
2. A paint can is a right circular cylinder with a radius of 3.5 inches and a height of 7.5 inches. Find the volume of the paint can. Round your answer to the nearest hundredth. (
   Solution

   x

   Solution:
   \(288.63 \text{ in}^{3}\) (when using the pi button on the calculator)
   )
3. A water tower is used to pressurize the water supply for the distribution of water in the surrounding area. A particular water tower is in the shape of a right circular cylinder with a radius of 4.25 meters and a height of 7.5 meters. Find the volume of the water tower. Round your answer to the nearest whole number. (
   Solution

   x

   Solution: \(426 \: {\text{m}}^{3}\) (when using the pi button on the calculator)
   Details:
   
   
   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 \(π\) 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. A 55-gallon drum is in the shape of a right circular cylinder with a diameter of 22.5 inches and a height of 33.5 inches. First, find the radius of the drum and then use the radius to find the volume of the drum. Round your answer to the nearest hundredth. (
   Video Solution

   x

   Solution:
   \(\text{Radius} = 11.25 \text{ in}\)
   \(\text{Volume} = 13319.86 \text{ in}^{3}\) (when using the pi button on the calculator)
   Details:
   

   
   (Video Source | Transcript)
   )
5. A support column on a building is a right circular cylinder. It has a radius of 1.5 feet and a height of 16 feet. Find the volume of the column. Round your answer to the nearest whole number. (
   Solution

   x

   Solution: \(113 \text{ ft}^{3}\) (when using the pi button on the calculator)
   Details:
   
   
   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 \(1.5 {\text{ft}} \times 1.5 {\text{ft}}\) 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 \(\text{ft}\) 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 \(π\) 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. A triple-A battery is a right circular cylinder with a radius of 5.25 mm and a height of 44.5 mm. Find the volume of the battery. Round to the nearest tenth. (
   Video Solution

   x

   Solution: \(3853.3 \text{ mm}^{3}\) (when using the pi button on the calculator)
   Details:
   

   
   (Video Source | Transcript)
   )

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