Back
Volume of a Right Circular Cylinder
> ... Math > Circles and Pi > Volume of a Right Circular Cylinder

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.

Volume of a Right Circular Cylinder

Let $$r = radius$$ and $$h = height$$

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

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

(Video Source | Transcript)
)

## Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.