How to Calculate the Volume of a Sphere with a Diameter of 36 cm: A Step-by-Step Guide
Introduction
The volume of a sphere is an important concept in geometry, with applications in various fields such as physics, engineering, and everyday problem-solving. In this article, we'll explore how to calculate the volume of a sphere when given its diameter of 36 cm. We'll break down the process step by step, including the formulas used and specific calculations.
Understanding the Formula for the Volume of a Sphere
The volume V of a sphere is given by the formula:
V (frac{4}{3}) π r3
Where:
V is the volume of the sphere π (pi) is approximately 3.14159 (often rounded to 3.14 for simplicity) r is the radius of the sphereStep-by-Step Calculation
Step 1: Determine the Radius
The radius r is half of the diameter. Given a diameter of 36 cm, we can calculate the radius:
r (frac{36;{rm{cm}}}{2}) 18;{rm{cm}}
Step 2: Substitute the Radius into the Formula
Now that we have the radius, we can substitute it into the volume formula:
V (frac{4}{3}) π (18;{rm{cm}})^3
Step 3: Calculate the Cubed Radius
First, calculate the cube of the radius:
(18;{rm{cm}})^3 5832;{rm{cm}}^3
Step 4: Substitute the Cubed Radius into the Formula
Now substitute this value back into the volume formula:
V (frac{4}{3}) π 5832;{rm{cm}}^3
Step 5: Calculate the Volume
Assuming π is approximately 3.14:
V (frac{4}{3} times 5832 times 3.14;{rm{cm}}^3
V ≈ 7764 times 3.14;{rm{cm}}^3
V ≈ 24360.76;{rm{cm}}^3
Verification and Additional Insights
The volume calculated is approximately 24360.76 cm3. It's important to note that this is an approximation, as π is a transcendental number and cannot be expressed exactly as a simple fraction of integers.
For a more precise calculation, you can use the value of π provided by your calculator or a mathematical software tool. However, for most practical purposes, the approximation is sufficient.
Additional Calculations and Considerations
Another way to approach the problem is to use the diameter directly in the formula:
V (frac{4}{3}) π (frac{36}{2})^3 (frac{4}{3}) π 18^3 (frac{4}{3}) π 5832;{rm{cm}}^3
This yields the same result as the previous method.
Conclusion
In conclusion, the volume of a sphere with a diameter of 36 cm is approximately 24360.76 cm3. This method and approach can be applied to any spheres with known diameters or radii. Understanding these calculations is crucial for various applications in science, engineering, and everyday problem-solving.