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.
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