Como Calcular O Peso De Um Cilindro

Calculating the weight of a cylinder is essential in engineering, construction, and manufacturing. This guide explains the formula, provides a practical calculator, and offers real-world examples to help you determine the weight of cylindrical objects accurately.

How to calculate the weight of a cylinder

The weight of a cylinder depends on its dimensions, material, and the density of the material. To calculate the weight, you need to know the volume of the cylinder and the density of the material. The formula for the volume of a cylinder is:

Volume (V) = π × r² × h

Where:

r = radius of the cylinder
h = height of the cylinder
π = pi (approximately 3.14159)

Once you have the volume, you can calculate the weight by multiplying the volume by the density of the material. The formula for weight is:

Weight (W) = Volume × Density

Where:

Density (ρ) = mass per unit volume of the material

For example, if you have a steel cylinder with a radius of 5 cm and a height of 10 cm, and the density of steel is 7.85 g/cm³, you can calculate the weight as follows:

Example:

Volume = π × (5 cm)² × 10 cm = π × 25 cm² × 10 cm = 785.4 cm³

Weight = 785.4 cm³ × 7.85 g/cm³ = 6,170.6 g = 6.17 kg

Formula for cylinder weight

The complete formula for calculating the weight of a cylinder is:

Weight (W) = π × r² × h × ρ

Where:

W = weight of the cylinder
r = radius of the cylinder
h = height of the cylinder
ρ = density of the material
π = pi (approximately 3.14159)

This formula combines the volume calculation with the density to give you the weight directly. You can use this formula in the calculator provided or in your own calculations.

Worked example

Let's work through a practical example to illustrate how to calculate the weight of a cylinder.

Example 1: Aluminum Cylinder

Suppose you have an aluminum cylinder with the following dimensions:

Radius (r) = 3 cm
Height (h) = 8 cm
Density of aluminum (ρ) = 2.7 g/cm³

Using the formula:

Weight (W) = π × (3 cm)² × 8 cm × 2.7 g/cm³

W = π × 9 cm² × 8 cm × 2.7 g/cm³

W = π × 72 cm³ × 2.7 g/cm³

W ≈ 3.14159 × 72 × 2.7 ≈ 615.75 g ≈ 0.616 kg

So, the weight of the aluminum cylinder is approximately 0.616 kg.

Example 2: Steel Cylinder

Now, let's consider a steel cylinder with these specifications:

Radius (r) = 4 cm
Height (h) = 12 cm
Density of steel (ρ) = 7.85 g/cm³

Using the formula:

Weight (W) = π × (4 cm)² × 12 cm × 7.85 g/cm³

W = π × 16 cm² × 12 cm × 7.85 g/cm³

W = π × 192 cm³ × 7.85 g/cm³

W ≈ 3.14159 × 192 × 7.85 ≈ 4,752.96 g ≈ 4.75 kg

Therefore, the weight of the steel cylinder is approximately 4.75 kg.

FAQ

What units should I use for the radius and height?: You can use any consistent units for the radius and height, such as centimeters, meters, or inches. Just make sure the units for the radius and height are the same.
How do I find the density of a material?: The density of a material can usually be found in reference tables or material datasheets. It's important to use the correct density for accurate weight calculations.
Can I use this formula for hollow cylinders?: No, this formula is for solid cylinders. For hollow cylinders, you would need to subtract the weight of the material removed to form the hollow space.
What if my cylinder is not perfectly straight?: If the cylinder is not perfectly straight, the actual weight might be slightly different due to variations in the material or dimensions. The formula assumes a perfect cylinder.
How accurate is this calculation?: The calculation is accurate as long as you have precise measurements of the radius, height, and density. Small measurement errors can affect the final result.