Volume of a Sphere
Overview
This section delves into the measurement of the volume of a sphere, illustrating the process through practical experimentation. By immersing a sphere in a container of water, we explore the concept of volume in relation to water displacement.
Key Points
- Experiment for Volume Measurement: The practical experiment involves putting spheres of various radii into a full container of water, causing the water to overflow. By measuring the water displaced, we can estimate the sphere's volume.
- Volume Formula: From the experiment, we derive that:
Volume of a Sphere = \( \frac{4}{3} \pi r^3 \)
Where \( r \) is the radius of the sphere.
3. Volume of a Hemisphere: Since a hemisphere is half a sphere, its volume is derived as:
Volume of a Hemisphere = \( \frac{2}{3} \pi r^3 \)
Significance
Knowing the volume of spheres and hemispheres is integral in fields ranging from physics to engineering, where spherical objects are frequently encountered. The precise calculation of their volumes is essential for applications in design, manufacturing, and physical sciences.