What is the formula for calculating the volume of a cone?

What is the formula for calculating the volume of a cone?

• A. π × r² × h
• B. (1/3) × π × r² × h
• C. (1/2) × base area × height
• D. 2 × π × r² × h

Answer: (B)

The formula for calculating the volume of a cone is (1/3) × π × r² × h because it accounts for the three-dimensional shape of the cone. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height from the base to the tip. The factor of (1/3) indicates that the cone's volume is one-third of the volume of a cylinder that has the same base area (π × r²) and height (h). This relationship arises from the geometric properties of these shapes; specifically, a cone can be thought of as tapering down to a point, unlike a cylinder which maintains a consistent cross-section throughout. This formula derives from integral calculus and geometry, and it effectively captures the unique nature of the cone, making it essential for accurately calculating its volume in various applications such as engineering and architecture.

The formula for calculating the volume of a cone is (1/3) × π × r² × h because it accounts for the three-dimensional shape of the cone. In this formula, 'r' represents the radius of the base of the cone, and 'h' represents the height from the base to the tip.

The factor of (1/3) indicates that the cone's volume is one-third of the volume of a cylinder that has the same base area (π × r²) and height (h). This relationship arises from the geometric properties of these shapes; specifically, a cone can be thought of as tapering down to a point, unlike a cylinder which maintains a consistent cross-section throughout.

This formula derives from integral calculus and geometry, and it effectively captures the unique nature of the cone, making it essential for accurately calculating its volume in various applications such as engineering and architecture.