Volume of Circle

Since a circle is a 2-dimensional shape, it does not have volume. However, when we extend a circle into the third dimension to form a sphere, we can talk about the volume.

The volume of a sphere is calculated using the formula:
Volume = (4/3) × π × r³

Here, r is the radius of the sphere.

A sphere is a perfectly symmetrical 3-dimensional shape, like a ball.
To calculate its volume, we take the radius and use the formula involving π (pi), which is approximately 3.14159.

To derive the volume of a sphere, we start with the concept of volume as the total space occupied by a 3D object.

The formula for the volume of a sphere is:

Volume = (4/3) × π × r³

This formula:

• Uses r, the radius of the sphere.

• Includes π to account for the circular symmetry of the sphere.

• Incorporates the factor 4/3, which arises from the integration process used in calculus to sum up the infinite thin circular disks that form the sphere.

Although this formula is rooted in integral calculus, it can also be appreciated conceptually as a way to measure how much space is inside a perfectly round 3D shape.

The volume of a sphere is always expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

To find the volume, follow these steps:

1. Measure the radius of the sphere.

2. Use the formula:
   Volume = (4/3) × π × r³

3. Substitute the radius value into the formula and perform the calculations.

This will give you the volume of the sphere in cubic units, representing the 3D space it occupies.

Remember the formula:
The formula for the volume of a sphere is:
Volume = (4/3) × π × r³

Break it down:

• The volume is the amount of space inside the sphere.

• The radius is the key measurement used to calculate that space.

Simplify the numbers:

• If the radius is a simple number like 2, 3, or 4, it's easier to cube it and calculate the volume.

Check for sphere roots:

• If you're given the volume and need to find the radius, rearrange the formula and take the cube root to solve backward.

• Radius: The distance from the center of the sphere to any point on its surface. It is essential for calculating both volume and surface area.

• Volume: The amount of space enclosed within a 3D object.
  Formula for a sphere:
  V=43πr3V = \frac{4}{3} \pi r^3V=34​πr3

• Sphere: A 3-dimensional shape where all points on the surface are equidistant from the center — like a basketball or a globe.

• Cubic Units: Units used to measure volume.

  • If the radius is in centimeters (cm) → volume is in cubic centimeters (cm³).

  • If in meters (m) → volume is in cubic meters (m³).

• Pi (π): A mathematical constant used in geometry, approximately equal to 3.14159, and common in formulas involving circles and spheres.

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