How to Calculate Cylinder Volume and Surface Area (+FREE Worksheet!)
The volume of a cylinder is V = πr²h, the area of the circular base times the height. Its surface area is SA = 2πr² + 2πrh: two circles plus the curved side. For a cylinder with radius 3 and height 5, V = π·9·5 = 45π ≈ 141.4 cubic units and SA = 18π + 30π = 48π ≈ 150.8 square units.
In this blog post, you learn how to find the volume and surface area of cylinders by using the volume and surface area formula.
Cylinder Surface Area and Volume: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Label the diagramWrite each given measurement on the figure.
- Choose the formulaMatch the formula to distance, midpoint, area, volume, or angle relationships.
- Check unitsUse linear, square, or cubic units as appropriate.
Worked examples
Find volume
- Use (V=pi r^2h).
- Substitute r = 3 and h = 10.
- Compute (9cdot10pi).
Use diameter
- Radius is 4.
- Use (V=pi r^2h).
- Compute (16cdot5pi).
Try one before moving on
Cylinder Surface Area and Volume: pop-up practice
Watch this practice video for additional examples and reinforcement:
Related Topics
- How Calculate the Area of Trapezoids
- How to Find the volume and surface area of Rectangular Prisms
- How to Solve Triangles Problems
- How to Find Volume and Surface Area of Cubes
- How to Find the Perimeter of Polygons
Step by step guide to calculating Cylinders volume and surface area
- A cylinder is a solid geometric figure with straight parallel sides and a circular or oval cross section.
- Volume of Cylinder Formula (= π) (radius)(^2 × ) height, ( π = 3.14)
- The surface area of a cylinder (=2πr^2+2πtext{ rh })
For education statistics and research
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Cylinder Volume and Surface Area, Example 1:
Find the volume and Surface area of the follow Cylinder.
Solution:
Use volume formula: Volume (= π) (radius)(^2 × ) height, ((r=2 text{ cm }, h=8 text{ cm }))
Then: Volume (=π(2)^2×8= 4π×8=32π)
(π=3.14) then: Volume (=32π=32 × 3.14 = 100.48) (text{ cm }^3 )
Use surface area formula: Surface area (=2πr^2+2πtext{ rh })
Then: (=2π(2)^2+2π(2)(8)=2π(4)+2π(16)=8π+32π=40π)
(π=3.14) then: Surface area (=40×3.14=125.6) (text{ cm }^2)
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Cylinder Volume and Surface Area, Example 2:
Find the volume and Surface area of the follow Cylinder. 
Solution:
Use volume formula: Volume (= π) (radius)(^2 × ) height, ((r=4 text{ cm }, h=6 text{ cm }))
Then: Volume (=π(4)^2×6= 16π×6=96π)
(π=3.14) then: Volume (=96π=96 × 3.14=301.44) (text{ cm }^3 )
Use surface area formula: Surface area (=2πr^2+2πtext{ rh })
Then: (=2π(4)^2+2π(4)(6)=2π(16)+2π(24)=32π+48π=80π)
(π=3.14) then: Surface area (=80×3.14=251.2) (text{ cm }^2)
Exercises for Calculating Cylinder Volume and Surface Area
Find the volume of each Cylinder. Round your answer to the nearest tenth. ((pi=3.14))
Download Cylinder Worksheet
- (color{blue}{75.4 m^3})
- (color{blue}{1,130.4 m^3})
- (color{blue}{1,808.6 m^3})
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