Mensuration: Cylinder, Cone, Sphere and Cuboid

The measurement of 2-dimensional and 3-dimensional geometrical figures can be called mensuration. It refers to that branch of geometry in which the measurement of length, area, the volume of 2-dimensional and 3-dimensional figures such as cone, cylinder etc is taken out.

Essential Terms Used in Mensuration

Some important terminologies used in mensuration include:

1. Area – This refers to the space occupied by a 2-dimensional closed figure.
2. Volume – Volume refers to the measure of a 3- dimensional closed figure.
3. Perimeter – The boundary of the closed figure is defined as the perimeter.
4. Total surface Area – The sum of both lateral and curved surface area is known as total surface area.
5. Lateral Surface Area – When one measures all sides of an object excluding the top and base is known as lateral surface area.
6. Curved Surface Area – The measurement of the area of a curved surface is known as curved surface area.

Cylinder

A 3-dimensional geometrical figure with a base and a top that are congruent and parallel to each other can form a cylinder. For example, a pipe, candle etc.

The formula for cylinder includes: –

Volume -( π * radius² * height ) cubic units.

Total surface area – (2π * radius * height + 2π * radius²) square units.

Lateral surface area – (2π * radius * height ) square units.

Cone 

A 3-dimensional geometrical shape formed by lines that meet at a common point is known as a cone. The common meeting point of lines or segments is called the apex. The base of the cone is circular which helps in finding its radius. The length of the cone from the apex to any point on the circumference of the base is a slant height. Examples of cone-shaped objects include party hats, traffic cones etc.

The formula for cone includes: –

Volume – (1/3 π * radius² * height ) cubic units.

Total Surface Area – (π*radius (radius + length) ) square units.

Sphere

A sphere can be defined as a completely round geometrical shape in 3- dimensional space. The distance from the centre to any point of the sphere is known as its radius. For example a ball, marbles etc.

The formula for sphere includes: –

Volume –( 4/3 *π * radius³   ) cubic units.

The surface area of a sphere – (4π * radius² ) square units.

Cuboid

A cuboid can be defined as a 3-dimensional figure when all sides are not equal. It has 6 faces, 8 vertices and 12 edges wherein all the faces are rectangles. For example a brick, mattress etcetera.

The formula for cuboid includes: –

Volume – (length*breadth*height) cubic units.

Lateral Surface Area – 2*height* (length + breadth) square units.

Total Surface Area – 2*(length*breadth + breadth*height + length*height) square units.

Diagonal length of cuboid – length² + breadth² + height² units.

The above-mentioned formulas help in understanding more about the 3-dimensional geometrical figures such as cylinder, cone, sphere and cuboid.

Conclusion

It can be concluded that mensuration refers to the measurement of 2-dimensional and 3-dimensional geometrical figures. The frequently used terms in mensuration are volume, total surface area, lateral surface area etcetera. The formula for measuring various 3-dimensional geometrical figures such as cylinder, cuboid, cone and sphere have been depicted here. The proper knowledge of these formulas can help in making the concepts of geometry easy and interesting.