Calculate cylinder properties including volume, lateral surface area, total surface area, and base area. Enter radius and height to get all measurements.
Volume
785.3982 cm^3
Real-world cylinder measurements
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
Volume
250pi cm^3
Lateral Surface
100pi cm^2
Base Area
25pi cm^2
Total Surface
150pi cm^2
Comparison: A cylinder has exactly 3 times the volume of a cone with the same base and height. Archimedes proved this relationship.
Volume
785.3982 cm^3
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.
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.
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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.
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
Volume
785.3982 cm^3