Density of a Sphere Calculator

Historical Background

Density is a fundamental property of matter that relates mass to volume. The concept of density has been utilized for centuries to describe materials and differentiate them based on their heaviness or lightness. This measurement became critical in physics, engineering, and materials science to analyze objects’ physical behavior.

Formula

The formula to calculate the density of a sphere involves the volume of a sphere and its mass:

\[ D = \frac{m}{\frac{4}{3}\pi r^3} \]

where:

• \(D\) is the density in kilograms per cubic meter (kg/m³),
• \(m\) is the mass of the sphere in kilograms,
• \(r\) is the radius of the sphere in meters.

Example Calculation

Suppose you have a sphere with a mass of 12 kg and a radius of 0.5 m. To calculate the density, we follow these steps:

1. Calculate the volume:

\[ V = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi (0.5)^3 \approx 0.5236 \text{ m}^3 \]

2. Calculate the density:

\[ D = \frac{12}{0.5236} \approx 22.91831 \text{ kg/m}^3 \]

Common FAQs

What is the density of a sphere?

• The density of a sphere is the total mass per unit of volume of a spherical object. It is expressed in kilograms per cubic meter (kg/m³).

How does mass affect density?

• If the mass increases while the volume remains the same, the density increases proportionally. Similarly, if the mass decreases, the density decreases.

Can the density of a sphere vary based on material?

• Yes, the density is inherently related to the type of material the sphere is composed of, so it will vary for different substances even with the same mass or volume.