Test: Representing 3-D in 2-D - Class 8 MCQ

A pentagonal pyramid has 5 triangular faces. One face is a pentagonal base, and the other four are triangular sides that connect the vertices of the pentagon to the apex.

A rectangular pyramid consists of 5 faces: one rectangular base and four triangular lateral faces. This structure demonstrates how different shapes can form a complex 3-D object.

A hexagonal prism has 12 vertices, which come from the two hexagonal bases (each with 6 vertices) and the connections between the corresponding vertices of the two bases.

The hexagonal prism has the highest number of faces among the options, with a total of 8 faces (2 hexagonal bases and 6 rectangular lateral faces). This variety allows for more complex geometric properties.

Euler's formula for polyhedrons is expressed as F - E + V = 2, where F is the number of faces, E is the number of edges, and V is the number of vertices. This relationship helps in verifying the properties of polyhedrons.

The correct representation of Euler's formula is F - E + V = 2. This formula is fundamental in topology and helps in classifying different types of polyhedra.

The formula F - E + V = 2 is used to verify whether a given set of faces, edges, and vertices corresponds to a valid polyhedron, confirming its geometric structure.

A polyhedron is defined as a three-dimensional shape that has flat polygonal faces and straight edges. Examples include cubes, pyramids, and prisms, which differ from shapes like spheres and cones that feature curved surfaces.

A hexagonal prism consists of 8 faces (2 hexagonal bases and 6 rectangular lateral faces), 12 edges, and 12 vertices. This structure highlights the properties of prisms and their base shapes.

The lateral faces of a triangular prism are rectangles. A triangular prism consists of two triangular bases and three rectangular lateral faces that connect the bases together.

A cuboid has 12 edges, which are formed by the intersection of its rectangular faces. Each edge corresponds to the connection between two vertices.

A tetrahedron has 6 edges. These edges connect the 4 vertices of the tetrahedron, forming the framework that defines its triangular faces.

A rectangular pyramid has 5 vertices: one at the apex and four at the corners of the rectangular base. This configuration supports the unique shape of the pyramid.

The primary purpose of a net is to help find the surface area of solids by laying out all the faces flat. This visualization aids in understanding the dimensions and calculations required for surface area.

A cube has 12 edges, which connect the vertices of its 6 square faces. The edges form the framework of the cube, allowing it to maintain its 3-D structure.

A pentagonal prism has 7 faces: two pentagonal bases and five rectangular lateral faces. This structure is essential for understanding the properties of prisms in geometry.

A tetrahedron has 4 faces, all of which are triangular. Each triangular face meets the other faces at the vertices, making it a simple polyhedron with a minimal number of faces.

A net is a two-dimensional shape that can be folded to form a three-dimensional solid. It shows all the faces of the solid laid out flat, facilitating visualization and calculation of surface area.

A cube has 6 faces, all of which are square. This uniformity in shape allows for a variety of applications in geometry and real-world structures.

A cylinder is not a polyhedron because it has curved surfaces, whereas polyhedra are defined by having flat faces and straight edges. All other options listed are polyhedra.