Volume Of A Cone Formula

Volume Of A Cone Formula

The area a cone takes up on a three-dimensional plane is known as its volume. A cone’s base is round, hence, it is formed of a radius and a diameter. The highest point of the cone, which is naturally at the bottom when it comes to ice cream, may then be reached from the centre of the base. This point is where the height of the cone is determined.

What is Volume of Cone?

The amount of room or capacity a cone takes up is known as its volume. Cones’ volume is expressed in cubic units such as cm3, m3, in3 etc. Any of a triangle’s vertices can be rotated to create a cone. A cone is a strong, round, three-dimensional shape. It has a surface that is curved. The perpendicular height is the distance from the base to the vertex. A cone can be classified as either an oblique cone or a right circular cone. In contrast to an oblique cone, which has a vertex that is not vertically above the centre of the base, the right circular cone has a vertex that is vertically above the centre of the base.

Volume of Cone Formula

The area of the conical base multiplied by the height of the cone is multiplied by one-third to get the volume of a cone. A cone can be thought of as a pyramid with a circular cross-section in terms of geometric and mathematical notions. Students can quickly determine a cone’s volume by measuring its height and radius. The volume of the cone is given as V = (1/3)r2h if the radius of the cone’s base is “r” and its height is “h.”

Volume of Cone With Height and Radius

Given a cone’s height and base radius, the volume of the cone may be calculated using the Volume Of A Cone Formula = (1/3)r2h cubic units.

Volume of Cone With Height and Diameter

Given a cone’s height and base diameter, the volume of the cone may be calculated using the Volume Of A Cone Formula = (1/12)d2h cubic units.

Volume of Cone With Slant Height

The Pythagorean theorem can be applied to the cone to determine the relationship between its volume and slant height.

It is aware that h2 + r2 = L2 h = (L2 – r2)

L is the cone’s slant height, r is the base’s radius, and h is the cone’s height.

Derivation of Volume of Cone Formula

The activity demonstrates how the volume of a cylinder may be used to calculate the volume of a cone. Take three cones, each with a height of “h,” a base radius of “r,” and a cylinder. The cones should be filled with water and then emptied one at a time.

One-third of the cylinder is filled by each cone. These three cones will therefore fill the cylinder. The volume of a cone is therefore equal to one-third that of a cylinder.

Cone volume equals to  (1/3) × πr2h = (1/3)πr2h

How to Find Volume of Cone?

Applying the Volume Of A Cone Formula, one can determine a cone’s volume given the necessary inputs. When the base radius or the base diameter, height, and slant height of the cone are determined, the next stages can be carried out.

Step 1: Write down the known parameters, “r” denoting the radius of the cone’s base, “d” denoting its diameter, “L” denoting its slant height, and “h” denoting its height.

Step 2: Use the Volume Of A Cone Formula to get the cone’s volume,

Cone volume using the base radius: V = (1/3)πr2h or (1/3)πr2√(L2 – r2)

Cone volume using the base diameter: V =(1/12)πd2h = (1/12)πd2√(L2 – r2)

Step 3: Convert the outcome to cubic units.

Volume of Cone Examples

A cone with a radius of “r” and a height of “2r” has a volume equal to that of a hemisphere with radius “r.” Consequently, (1/3)πr2(2r) = (2/3)πr3.

By multiplying the diameter by two to obtain the radius and plugging the result into the Volume Of A Cone Formula (1/3)πr2h, the volume of a cone may be computed.

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Practice Questions on Volume of Cone

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