Sphere Volume Calculation

1. Enter the "radius" of the sphere whose volume you want to calculate.
2. The "volume of the sphere" and "surface area of the sphere" will be automatically calculated.

A sphere (きゅう, Sphere) is the set of all points in three-dimensional space that are equidistant (radius) from a center point.

Characteristics of a Sphere

1. Center (O) - The point exactly in the middle of the sphere.
2. Radius (r) - The distance from the center to the surface of the sphere.
3. Diameter (d) - The longest distance from one end of the sphere to the other (diameter \( d = 2r \)).
4. Surface Area - The area of the sphere's surface can be calculated using the following formula:
   S = 4πr²
5. Volume - The volume inside the sphere can be calculated using the following formula:
   4 3 πr³

Examples of Spheres

• Earth and planets
• Soccer balls and ping pong balls
• Water droplets (which take on a nearly spherical shape due to surface tension)

Difference Between a Sphere and a Circle

	Sphere	Circle
Dimensions	3D	2D
Shape	Solid	Flat
Formulas	Requires calculation of volume and surface area	Requires calculation of area and circumference

A sphere is a 3D solid, while a circle is merely its 2D cross-section. For example, a ball is a sphere, but the surface of a coin is a circle.

The volume of a sphere can be calculated using the following formula:

Explanation

• V: Volume of the sphere
• r: Radius of the sphere
• π: Pi (approximately 3.14159)

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Example Calculation

Calculate the volume of a sphere with radius r = 5 cm

Therefore, the volume of a sphere with a radius of 5 cm is approximately 523.6 cm³.

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Key Points for Calculating the Volume of a Sphere

1. Cube the radius (r³)
2. Multiply by 4/3
3. Finally, multiply by π

The surface area of a sphere can be calculated using the following formula:

Explanation

• S: Surface area of the sphere
• r: Radius of the sphere
• π: Pi (approximately 3.14159)

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Example Calculation

Calculate the surface area of a sphere with radius r = 5 cm

Therefore, the surface area of a sphere with a radius of 5 cm is approximately 314.16 cm².

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Key Points for Calculating the Surface Area of a Sphere

1. Square the radius (r²)
2. Multiply by 4
3. Finally, multiply by π