Fundamentals of Geometry for 3D Shapes: Concepts and Principles

Aspiring designers must have a solid understanding of area and volume. Knowledge of the volumes is critical in form analysis, spatial perception, and problem-solving skills. This essential skill aids the ability to visualize and deal with 3D objects, making it relevant to the DAT ability test. The students who understand these concepts will provide a good foundation for making good fortunes in the design field. As for the perceptual value of the given 3D forms, it is helpful to solve critical questions from the NAT section, which contains relatively easy questions to score.

This Story also Contains

1. 1. Cube & Cuboid:
2. 2. Sphere and Hemisphere
3. 3. Cylinder
4. 4. Cone
5. 5. Pyramid
6. Sample Question Paper: UCEED 2024

3D Shapes Geometry and Their Properties:

Below is a breakdown of 3D shapes properties with specific examples. Understanding these Geometry of three-dimensional shapes enhances problem-solving abilities and spatial visualization in design tasks.

1. Cube & Cuboid:

Three-dimensional shapes that come under the class of polyhedral are stable solid bodies with flat faces. There are two crucial shapes known as the cube and the cuboid. These two shapes are identical in that they possess twelve edges, six faces and eight vertices; nevertheless, they are entirely dissimilar in size and shape.

Comparison of Cube and Cuboid

Note: All sides of the cube are equal, and the length taken is “a” units.

Similarly, for the cuboid, Length (l units), Breadth (b units) and Height (h units)

Knowing the fundamentals of 3D Geometry makes it simple to differentiate between the cube and cuboid characteristics and use them for creative endeavors.

2. Sphere and Hemisphere

Rounded solids include both hemispheres and spheres, which are three-dimensional shapes. They possess unique mathematical qualities and are frequently encountered in organic forms.

Sphere

A sphere is a three-dimensional object that is precisely spherical and has equal distances between each point on its surface and the center. It has no edges or vertices and is the three-dimensional equivalent of a circle.

Note: All points on the surface are equidistant from the center in a sphere.

Hemisphere

When a given sphere is cut along its diameter to reveal a hemisphere, which is precisely half of a sphere, its surface is curved, and its base is a flat circular face. Unlike a sphere, it has a boundary running along its circular base but no edges or vertices on its curved surface.

For a Hemi-Sphere

Note: A hemisphere with a flat surface is made by cutting a sphere from the center.

3. Cylinder

A three-dimensional geometric object called a cylinder comprises two parallel circular bases joined by a curved surface. One of the most prevalent 3D shapes properties can be found in many natural and artificial artefacts. The height in a cylinder is the vertical distance between two faces of the cylinder.

4. Cone

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of the base) called the apex or vertex. Cones are frequently visible in man-made and natural forms, such as volcanic mountains, ice cream cones etc.

For a cone with a height (h units), slant height (l) and base radius (r units)

5. Pyramid

A pyramid is a three-dimensional geometric form consisting of triangular faces that converge at a single point known as the apex or vertex and a polygonal base. The name of a pyramid is determined by the type of base, like a triangular, square or a based pyramid.

In a pyramid with a triangular base, for the given height (h), slant height (l) and having a triangular base, the area can be calculated as follows:

Pyramid: With a Triangular Base(3 sided base)

You may also check: Fundamental Geometry Concepts for 2D Shapes

Sample Question Paper: UCEED 2024