Volume of Cylinders formulas You Should Know - BYJUS

# Volume of Cylinders formulas

The volume of a shape is defined as the space occupied by a particular shape. The objects around us like a ball, a water bottle, and so on, have a specific volume. There are different formulas to calculate the volume of different shapes. Here we will focus on the formula used to calculate the volume of a cylinder.   ...Read MoreRead Less

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### List of Volume of Cylinder Formulas

The list below gives us the two formulas that are applied to calculate the volume of a cylinder. These two formulas will be elaborated further on.

1.  Volume of cylinder = Bh

2. Volume of cylinder = $$\pi r^2h$$

### Steps to find the product of mixed numbers

Follow these steps to multiply mixed numbers:

Step 1: The equivalent of mixed numbers can be represented by improper fractions. Hence, convert the mixed numbers to improper fractions.

Step 2: Multiply the respective numerators and write the product as the numerator of the resulting fraction. Similarly, multiply the denominators and write the product as the denominator of the resulting fraction.

Step 3: The resulting fraction is the product. This fraction can be further converted back into a mixed number as well.

### Volume of an Oblique Cylinder

An oblique cylinder is one that leans over. This indicates that the sides of the cylinder are not perpendicular to the base.

The formula for the volume of a right cylinder is also applied to calculate the volume of an oblique cylinder.

### Formula to find the volume of a cylinder

To calculate the volume of a cylinder, you need the radius or the diameter of the circular base, or the top, and the height of the cylinder.

The volume of the cylinder is the product of the area of the base and the height of the cylinder. The volume is measured in cubic units.

Mathematically, a cylinder’s volume can be expressed as:

Volume of the cylinder = Bh

Where,

• B = π$$r^2$$ is the “base area”

• h = The height of the cylinder

Therefore, we can use the formula,

Volume = $$\pi r^2h$$, to find the volume of a cylinder.

The above given formula is for both oblique and right cylinders.

### Visualizing the formula for the Volume of a cylinder

A cylinder can be visualized as a stack of circular discs that are placed on one another.

Remember, the area of a circle is π$$r^2$$, multiplying π$$r^2$$ by h which is the height of the stack of circles, results in  the volume of a cylinder, π$$r^2h$$.

### Solved Examples

Example 1: Find the volume of the cylinder with the given radius and height as 7cm and 10cm.

Solution:

Radius of the cylinder = 7 cm

Height of the cylinder = 10 cm

Volume of cylinder = π$$r^2h$$                   Write the formula for the volume

= π × $$(7)^2$$ × 10        Substitute

= 490 π                   Multiply

$$\approx$$ 1538.6                 Use a calculator

The volume is about 1538.6 cubic centimeters.

Example 2: Find the volume of the oblique cylinder with the given base area and height as 27.5$$in^2$$ and 13 in.

Solution:

Base area of the oblique cylinder = 27.5$$in^2$$

Height of the oblique cylinder    = 13 in

Volume of cylinder = Bh                 Write the formula for the volume

= 27.5 × 13        Substitute

= 357.5             Multiply

The volume of the oblique cylinder is 357.5$$~in^3$$

Example 3: How many gallons of water can a cylindrical water tank with base radius 15 cm and height 33.65 cm hold? (1 gallon = 3785.412$$cm^2$$)

Solution:

Radius of the cylindrical water tank = 15cm

Height of the cylindrical water tank = 33.65cm

Volume of cylinder = π$$r^2h$$                           Write the formula for the volume

= π × $$(15)^2$$ × 33.65        Substitute

= 7571.25π                      Multiply

$$\approx$$ 23773.725                  Use a calculator

The volume is about 23773.725 cubic centimeters.

1 gallon = 3785.412$$cm^3$$

Therefore 23773.7$$cm^3$$   = $$\frac{23773.7}{3785.412}$$ gallons

$$\approx$$ 6.28 gallons

The cylindrical water tank can hold approximately 6.28 gallonsof water.

Example 4: A cylindrical hazardous waste container has a diameter of 6.8 feet. The container can hold 945 gallons of hazardous waste. Find the height of the cylindrical container.

(1 ft $$\approx$$ 37.5 gal)

Solution:

Radius of the cylindrical container =$$\frac{\text{diameter}}{2}$$ = $$\frac{6.8}{2}$$ = 3.4 ft

Volume of the cylindrical container = 945 gal

1 ft $$\approx$$ 37.5 gal

Therefore 945 gal =$$\frac{945}{7.5} \approx$$ 126 ft3

Volume of the cylindrical container in cubic feet is 126 ft³.

Volume of cylinder = π$$r^2h$$                      Write the formula for the volume

126 = π × $$(3.4)^2$$ × h        Substitute

126 = 36.30 × h               Multiply

$$\frac{126} {36.30}$$ = $$\frac{36.30}{36.30}$$ × h                Division property

3.47 $$\approx$$ h                          Use a calculator

Therefore the height of the cylindrical container is approximately 3.47 ft.

Note : Using the formula for the volume of a cylinder, we can also find the height or the radius.

Frequently Asked Questions

A volume of a cylinder is used to measure the capacity of a cylinder and the amount of space it takes up.

The formula for the volume of a cylinder when the base area is given is,

Volume of a cylinder = Bh, where, B = πr2

The volume of a cylinder of base radius “r” and height “h” is

“V = πr2h. We know that r = d/2. By substituting this in the above formula, V = (1/4)πd2h.

A cylinder whose sides are slanted instead of being perpendicular to its base is called an oblique cylinder.

Yes, the formula for volume of Oblique and right cylinder are same and it is, Volume = πr2h