What does the formula V=4/3πr³ represent?

What does the formula V=4/3πr³ represent?

• A. The surface area of a sphere
• B. The volume of a sphere
• C. The circumference of a sphere
• D. The diameter of a sphere

Answer: (B)

The formula V = 4/3πr³ represents the volume of a sphere. This formula derives from the principles of geometry related to three-dimensional objects, specifically spheres. In this equation, 'V' denotes the volume, 'r' is the radius of the sphere, and π (pi) is a constant approximately equal to 3.14159. The term 4/3πr³ is used to calculate the amount of space contained within the sphere. The cubic nature of the radius (r³) in the formula indicates that volume is a measure of three-dimensional capacity, as opposed to surface area or circumference, which are measured in square and linear units, respectively. In contrast, the surface area of a sphere would use the formula 4πr², the circumference is represented by the formula 2πr, and the diameter is simply twice the radius (2r). Thus, the context and structure of the formula clearly identify it as a calculation for volume.

The formula V = 4/3πr³ represents the volume of a sphere. This formula derives from the principles of geometry related to three-dimensional objects, specifically spheres. In this equation, 'V' denotes the volume, 'r' is the radius of the sphere, and π (pi) is a constant approximately equal to 3.14159.

The term 4/3πr³ is used to calculate the amount of space contained within the sphere. The cubic nature of the radius (r³) in the formula indicates that volume is a measure of three-dimensional capacity, as opposed to surface area or circumference, which are measured in square and linear units, respectively.

In contrast, the surface area of a sphere would use the formula 4πr², the circumference is represented by the formula 2πr, and the diameter is simply twice the radius (2r). Thus, the context and structure of the formula clearly identify it as a calculation for volume.