Volume Calculator

How to Calculate Volume

Volume is a measure of the amount of space occupied by a three-dimensional object. The method for calculating volume depends on the shape of the object. Here's a comprehensive guide on how to calculate the volume of various 3D shapes:

Volume Formulas

• Cube: \(V = s^3\), where \(s\) is the length of a side
• Sphere: \(V = \frac{4}{3}\pi r^3\), where \(r\) is the radius
• Cylinder: \(V = \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height
• Cone: \(V = \frac{1}{3}\pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height

Calculation Steps

1. Identify the shape of the object
2. Measure the necessary dimensions (side length, radius, height, etc.)
3. Choose the appropriate formula for the shape
4. Substitute the measured values into the formula
5. Perform the calculations to find the volume

Example Calculation

Let's calculate the volume of a cylinder with radius 5 cm and height 10 cm:

1. Identify the shape: Cylinder
2. Measure dimensions: radius (r) = 5 cm, height (h) = 10 cm
3. Formula for cylinder: \(V = \pi r^2 h\)
4. Substitute values: \(V = \pi \times 5^2 \times 10\)
5. Calculate: \(V = 3.14159 \times 25 \times 10 = 785.4 \text{ cm}^3\)

Therefore, the volume of the cylinder is approximately 785.4 cubic centimeters.

Visual Representation

This diagram illustrates a cylinder with radius 5 cm and height 10 cm. The volume of this cylinder is approximately 785.4 cubic centimeters.