Cylinder Calculator
Calculate cylinder properties including volume, lateral surface area, total surface area, and base area. Enter radius and height to get all measurements.
V = pir^2h | A = 2pir(r + h)Cylinder Properties
Volume
785.3982 cm^3
3D Visualization
Cylinder Dimensions
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Real-world cylinder measurements
All Cylinder Properties
Radius (r)
5 cm
Diameter (d)
10 cm
d = 2r
Height (h)
10 cm
Volume (V)
785.3982 cm^3
V = pir^2h
Lateral Surface Area
314.1593 cm^2
A = 2pirh
Base Area
78.5398 cm^2
A = pir^2
Total Surface Area
471.2389 cm^2
A = 2pir(r + h)
Circumference
31.4159 cm
C = 2pir
Exact Values (in terms of pi)
Volume
250pi cm^3
Lateral Surface
100pi cm^2
Base Area
25pi cm^2
Total Surface
150pi cm^2
Cylinder Formulas
Basic Formulas
- Volume: V = pir^2h
- Lateral Area: A = 2pirh
- Base Area: A = pir^2
- Total Area: A = 2pir(r + h)
- Circumference: C = 2pir
Derived Formulas
- r from V: r = sqrt(V / (pi x h))
- h from V: h = V / (pir^2)
- Hollow V: pi x h x (R^2 - r^2)
- Diagonal: d = sqrt(4r^2 + h^2)
Comparison: A cylinder has exactly 3 times the volume of a cone with the same base and height. Archimedes proved this relationship.
Cylinder Properties
Volume
785.3982 cm^3
?How to Calculate Cylinder Properties
Cylinder formulas: Volume = pi x r^2 x h (pi r squared times height). Lateral Surface Area = 2 x pi x r x h (the curved side). Total Surface Area = 2 x pi x r x (r + h) (curved side plus two circular bases). Base Area = pi x r^2. A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.
What is a Cylinder?
A cylinder is a three-dimensional geometric shape consisting of two parallel circular bases connected by a curved surface at a fixed distance (height). Common examples include cans, pipes, tubes, and pillars. In a right cylinder, the bases are directly above each other; in an oblique cylinder, one base is offset. The volume measures the space inside, while surface area includes both the curved lateral surface and the two circular ends.
Key Facts About Cylinders
- Volume = pi x r^2 x h (base area times height)
- Lateral Surface Area = 2 x pi x r x h (the curved side only)
- Total Surface Area = 2 x pi x r x (r + h) or 2pir^2 + 2pirh
- Base Area = pi x r^2 (same as a circle)
- Circumference = 2 x pi x r (the perimeter of the circular base)
- Hollow cylinder volume = pi x h x (R^2 - r^2) where R is outer, r is inner radius
- A cylinder unfolded creates a rectangle (for lateral surface) plus two circles
- The height is the perpendicular distance between the two bases
Practice Cylinder Problems
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Practice with 4 problems to test your understanding.
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Quick Answer
Cylinder formulas: Volume = pi x r^2 x h (pi r squared times height). Lateral Surface Area = 2 x pi x r x h (the curved side). Total Surface Area = 2 x pi x r x (r + h) (curved side plus two circular bases). Base Area = pi x r^2. A cylinder is a 3D shape with two parallel circular bases connected by a curved surface.
Frequently Asked Questions
The volume of a cylinder is V = pir^2h, where r is the radius and h is the height. This is simply the area of the circular base (pir^2) multiplied by the height. For a cylinder with radius 5 and height 10, V = pi x 25 x 10 = 785.4 cubic units.
The lateral surface area is the area of the curved side of the cylinder, not including the circular bases. The formula is A = 2pirh. If you "unroll" this surface, it becomes a rectangle with width = circumference (2pir) and height = h.
Total surface area includes the curved lateral surface plus both circular bases: SA = 2pir^2 + 2pirh = 2pir(r + h). The first term (2pir^2) is for the two bases; the second (2pirh) is the lateral surface.
For a hollow cylinder (like a pipe), the volume is V = pih(R^2 - r^2), where R is the outer radius, r is the inner radius, and h is the height. This gives the volume of the material, not the empty space inside.
An oblique cylinder has bases that are not directly above each other - it "leans" to one side. The volume formula is the same (V = pir^2h, where h is the perpendicular height), but the lateral surface area calculation is more complex.
A cone with the same base and height as a cylinder has exactly 1/3 the volume. Cone: V = (1/3)pir^2h. Cylinder: V = pir^2h. This 3:1 ratio is a fundamental relationship in geometry.
Rearrange the volume formula: r = sqrt(V / (pi x h)). For example, if V = 314.16 and h = 10, then r = sqrt(314.16 / 31.416) = sqrt(10) = 3.16.
Common cylindrical objects include cans, pipes, tubes, pillars, drums, batteries, drinking glasses, silos, and tanks. Understanding cylinder calculations helps with problems like how much paint to cover a tank, or how much liquid a container holds.
Last updated: 2025-01-15
Cylinder Properties
Volume
785.3982 cm^3