Calculating the Volume of a Sphere with a Diameter of 30 cm

When dealing with geometric shapes, one of the most common calculations is determining the volume. For a sphere, the volume formula is essential. Let's explore how to find the volume of a sphere with a diameter of 30 cm step-by-step.

Introduction

A sphere is a three-dimensional object, and its volume can be calculated using the formula 4/3πr3, where r is the radius of the sphere. The diameter, D, is twice the radius (i.e., r D/2).

Problem

Given: Sphere with a diameter of 30 cm.

Find: Volume V.

Step-by-Step Calculation

The formula to calculate the volume of a sphere is:

[@ Math formula: V 4/3πr3]

To start, determine the radius (r) from the given diameter (D):

[@ Math formula: r D/2 30 cm / 2 15 cm]

Now, substitute the value of the radius into the volume formula:

[@ Math formula: V 4/3π(153) 4/3π(3375) ≈ 41125π cm3]

Using the approximation π ≈ 3.1416 for a more precise calculation:

[@ Math formula: V 14137.1669 cm3

This can be simplified to approximately 14137.2 cm3.

Conclusion

The calculation shows that the volume of a sphere with a diameter of 30 cm is approximately 14137.2 cm3. It's important to note that the π (pi) value can be approximated or taken from a more accurate source for precise results.

Additional Information

Understanding the formula and its application is crucial for solving problems related to geometric shapes in mathematics and physics. The formula for the volume of a sphere is widely used in various fields, from simple school problems to complex engineering calculations.

Other Related Calculations

Hemisphere:
If a hemisphere has a radius of 30 cm, its volume can be calculated using the formula for half of a sphere’s volume. The formula for the volume of a hemisphere is (frac{2}{3} pi r^3). [@ Math formula: V frac{2}{3} pi (303) 56571.428 cm3]

General Formula:
For any sphere, the volume can be calculated as follows: - Given a diameter D, the radius r D / 2. - Substitute r into the formula: V (frac{4}{3} pi r^3). - Alternatively, if you prefer, the volume formula can be expressed as V (frac{πD^3}{6}).

These formulas provide a comprehensive approach to solving similar volume problems involving spheres and hemispheres.