Volume of Cylinder Using Radius and Height
Volume of Cylinder measures the space enclosed by a cylindrical solid. Its volume is calculated using V = πr²h, where r is the radius and h is the perpendicular height. This page covers the formula, unit conversions, solved volume of cylinder examples, ratios and common aptitude problems.
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What Is the Volume of a Cylinder?
A cylinder has two equal circular bases. First calculate the base area as πr², then multiply it by the height. If the diameter d is given, use r = d/2, so V = π(d/2)²h = πd²h/4. Volume is measured in cubic units such as cm³, m³ or litres.
Volume of Cylinder Video Lessons
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Cylinder Volume and Surface Area
Learn how to calculate a cylinder’s volume, curved surface area (CSA), and total surface area (TSA) using the relevant mensuration formulas.
Volume of Cylinder Formula & Tricks
Important Formulas
Multiply the area of the circular base, πr², by the perpendicular height h.
Use this form when the diameter d is given because r = d/2.
R is the outer radius, r is the inner radius and h is the height.
Convert the calculated cubic volume into the required capacity unit.
Quick Tricks
When diameter is given, avoid a separate radius step by using V = πd²h/4.
For cylinders with the same height, volumes are proportional to the squares of their radii. For different dimensions, use V₁:V₂ = r₁²h₁:r₂²h₂.
Radius and height must be expressed in the same unit before applying the formula. The answer then has the corresponding cubic unit.
Volume of Cylinder Concepts
Applying the Cylinder Volume Formula
Use V = πr²h. If π = 22/7 is suitable, cancel factors before multiplying to reduce calculation. For r = 7 cm and h = 10 cm, V = (22/7) × 7² × 10 = 1540 cm³.
Using Diameter Instead of Radius
The radius is half the diameter. Squaring the diameter gives d², and the factor 1/4 accounts for the conversion from diameter to radius squared.
Unit Conversion and Capacity
Use 1 cm³ = 1 mL, 1000 cm³ = 1 L and 1 m³ = 1000 L. Convert all dimensions to one unit before calculating. A volume of 5500 cm³ is equal to 5500 mL or 5.5 L.
Volume of a Hollow Cylinder
For outer radius R, inner radius r and common height h, use V = π(R² − r²)h. This formula gives the volume of the cylindrical shell, not the empty space inside it.
Volume Ratios of Cylinders
Radius changes affect volume quadratically, while height changes affect volume linearly. Thus, doubling the radius makes the volume four times as large if height remains unchanged.
Volume of Cylinder Visual Guide
Use the diagram or chart below to understand the concept clearly.
Cylinder with radius and height
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Volume of Cylinder Revision Points
Recall these formulas, conversions and ratio rules for cylinder volume problems.
- Volume of a cylinder: V = πr²h.
- If diameter d is given: V = πd²h/4.
- Radius and height must be in the same unit before substitution.
- Volume is measured in cubic units.
- 1 cm³ = 1 mL, 1000 cm³ = 1 L and 1 m³ = 1000 L.
- Hollow-cylinder volume: π(R² − r²)h.
- For equal heights, cylinder volumes are proportional to the squares of their radii.
Volume of Cylinder FAQs
What is the volume of cylinder formula?
The formula is V = πr²h, where r is the radius and h is the perpendicular height.
How do you find the volume of a cylinder when its diameter is given?
Use V = πd²h/4, where d is the diameter and h is the height. This follows from r = d/2.
What is the volume of a cylinder with radius 7 cm and height 4 cm?
Using π = 22/7, V = (22/7) × 7² × 4 = 616 cm³.
How is cylinder volume converted from cubic centimetres to litres?
Divide the volume in cm³ by 1000. For example, 7500 cm³ = 7.5 litres.
What happens to the volume if the radius of a cylinder is doubled?
The volume becomes four times the original volume if the height remains constant, because volume is proportional to r².
What is the formula for the volume of a hollow cylinder?
Use V = π(R² − r²)h, where R is the outer radius, r is the inner radius and h is the height.