Sphere Density Calculator

Mass (\( m \)):

Volume (\( V \)):

Density (\( \rho \)):

Radius (\( r \)):

1. What is the Sphere Density Calculator?

Definition: This calculator computes the density (\( \rho \)) and radius (\( r \)) of a sphere based on its mass (\( m \)) and volume (\( V \)).

Purpose: It is used in physics, engineering, and materials science to determine the density and radius of spherical objects, such as planets, balls, or other spherical structures.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\( \rho = \frac{m}{V} \)

\( r = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \)

Where:

\( \rho \): Density (g/cm³, kg/m³, g/m³, kg/cm³, lb/cu ft);
\( m \): Mass (g, kg, mg, µg, dag, oz, lb);
\( V \): Volume (cm³, m³, L, mm³, in³, ft³);
\( r \): Radius (m, cm, mm, in, ft).

Steps:

Enter the mass (\( m \)) with its unit.
Enter the volume (\( V \)) with its unit.
Convert mass to grams and volume to cm³.
Calculate the density using \( \rho = \frac{m}{V} \).
Calculate the radius using \( r = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \).
Convert the results to the selected output units.
Display the results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Sphere Density and Radius Calculation

Calculating the density and radius of a sphere is crucial for:

Physics Education: Understanding material properties and spherical geometry.
Astronomy: Estimating the density of celestial bodies like planets.
Engineering Design: Analyzing spherical objects like ball bearings or storage tanks.

4. Using the Calculator

Example 1: Calculate the density and radius with \( m = 100 \, \text{g} \), \( V = 50 \, \text{cm}^3 \):

Mass: \( m = 100 \, \text{g} \);
Volume: \( V = 50 \, \text{cm}^3 \);
Density: \( \rho = \frac{100}{50} = 2 \, \text{g/cm}^3 \);
Radius: \( r = \left( \frac{3 \times 50}{4\pi} \right)^{\frac{1}{3}} \approx 2.287 \, \text{cm} \);
Result (Density in g/cm³): \( \rho = 2.0000 \, \text{g/cm}^3 \);
Result (Radius in cm): \( r = 2.2870 \, \text{cm} \).

Example 2: Calculate the density and radius with \( m = 1 \, \text{kg} \), \( V = 0.001 \, \text{m}^3 \):

Mass: \( m = 1 \, \text{kg} \times 1000 = 1000 \, \text{g} \);
Volume: \( V = 0.001 \, \text{m}^3 \times 1000000 = 1000 \, \text{cm}^3 \);
Density: \( \rho = \frac{1000}{1000} = 1 \, \text{g/cm}^3 \);
Radius: \( r = \left( \frac{3 \times 1000}{4\pi} \right)^{\frac{1}{3}} \approx 6.203 \, \text{cm} \);
Result (Density in kg/m³): \( \rho = 1000.0000 \, \text{kg/m}^3 \);
Result (Radius in m): \( r = 0.0620 \, \text{m} \).

5. Frequently Asked Questions (FAQ)

Q: What is the density of a sphere?
A: Density (\( \rho \)) is the mass per unit volume of a sphere, calculated as mass divided by volume.

Q: How is the radius calculated?
A: The radius (\( r \)) is calculated using the volume of a sphere formula, \( r = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \).

Q: Can this calculator handle any spherical object?
A: Yes, as long as the mass and volume are known, the calculator can determine the density and radius for any spherical object.