Cylinder Volume Calculator

Select Shape:

Radius \( r \):

Height \( h \):

External Diameter \( D \):

Internal Diameter \( d \):

Height \( h \):

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³): Volume (L):

1. What is a Cylinder Volume Calculator?

Definition: This calculator computes the volume of a solid cylinder or a hollow cylinder (cylindrical shell). A solid cylinder is a three-dimensional object with a circular base and uniform height, while a hollow cylinder is bounded by two right circular cylinders with the same axis and parallel annular bases (e.g., a pipe or straw).

Purpose: Useful in engineering, manufacturing, and design for determining the volume of cylindrical objects.

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ V_{\text{solid cylinder}} = h \cdot \pi \cdot r^2 \] \[ V_{\text{hollow cylinder}} = \pi \cdot h \cdot \frac{(D^2 - d^2)}{4} \]

Notes: The hollow cylinder volume represents the material between the inner and outer surfaces (e.g., the wall of a pipe). To find the volume inside a hollow cylinder, use the solid cylinder formula with the internal radius.

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)

Explanation: All dimensions are converted to cm, the volume is calculated in cm³, and then converted to in³, ft³, m³, and L.

3. Importance of Cylinder Volume Calculation

Details: Calculating the volume of cylinders is essential in engineering (e.g., designing pipes, tanks), manufacturing (e.g., rolls of material), and packaging.

4. Using the Calculator

Tips: Select the shape (Solid Cylinder or Hollow Cylinder), then enter the required dimensions (radius and height for a solid cylinder; external diameter, internal diameter, and height for a hollow cylinder) in mm, cm, m, in, or ft (all must be >0, with external > internal for hollow cylinders). The result shows the volume in cm³, in³, ft³, m³, and L.

5. Example

Given (Hollow Cylinder): External diameter \( D = 11 \, \text{cm} \), internal diameter \( d = 4 \, \text{cm} \), height = 9 cm.
Volume Calculation: \( V = \pi \cdot 9 \cdot \frac{(11^2 - 4^2)}{4} = \pi \cdot 9 \cdot \frac{(121 - 16)}{4} = \pi \cdot 9 \cdot 26.25 \approx 742.2 \, \text{cm}^3 \).
Given (Solid Cylinder): Radius \( r = 5 \, \text{cm} \), height = 10 cm.
Volume Calculation: \( V = 10 \cdot \pi \cdot 5^2 = 10 \cdot \pi \cdot 25 \approx 785.398 \, \text{cm}^3 \).

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